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THE  LIBRARY 
OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 

John  S.Prell 


I.I 

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I'"'.    ' 


r^t). 


STEAM-TUEBINES 


BY 

GAEL  C.   THOMAS 

^  -Professor  of  Marine  Engineering,  Sibley  College,  Cornell  University 


THIRD  EDITION,  REVISED  AND  ENLARGED 
FIRST  THOUSAN"D 

NEW   YORK 

JOHN  WILEY   &  SONS 

London:   CHAPMAN   &    HALL,    Limited 

1907 


Copyright,  1906.  1907 

BY 

CARL  C.  THOMAS 


ROBERT   DRUMMOND,   PRINTER,    NEW    YORK 


library 

735 


PREFACE. 


In  writing  this  book  I  have  aimed  to  give  in  logical  order 
the  fundamental  principles  of  steam-turbine  design,  with 
examples  of  their  application,  and  to  show  the  results  obtained 
in  engineering  practice. 

The  development  of  the  steam-turbine  has  been  so  rapid 
that  many  of  the  problems  involved,  while  solved  more  or 
less  satisfactorily  for  constructive  purposes,  have  not  been 
put  upon  a  scientific  basis.  Foremost  among  these  problems 
is  that  of  the  velocity  of  steam-flow  under  given  conditions, — 
important  not  only  for  an  understanding  of  the  operation  of 
the  turbine,  but  for  predicting  the  results  to  be  expected  from 
a  given  set  of  conditions.  ]\Iy  principal  incentive  has  been 
the  desire  to  analyze  and  correlate  the  results  of  certain  im- 
portant experimental  investigations,  and  to  show  how  these 
results  could  be  used  in  connection  with  the  well-known  laws 
of  hydraulics  and  thermodynamics  as  applied  to  steam-tur- 
bines. In  stating  these  laws  I  have  attempted  to  develop  the 
expressions  in  a  simple  and  direct  manner,  and  to  give  numer- 
ical and  graphical  solutions  illustrating  the  principles  involved. 

The  book  is  not  intended  to  be  or  to  take  the  place  of  a 
treatise  on  either  hydrauHcs  or  thermodynamics,  but  it  has 
seemed  best  to  give  in  outline  the  development  of  such  parts  of 
those  subjects  as  are  most  necessar}-  for  acquiring  the  working 
knowledge  which  it  is  the  ob.iect  of  the  book  to  impart.    I  have 

iii 


733420 


IV  PREFACE. 

attempted,  therefore,  to  discriminate  between  essential  princi- 
ples and  such  discussions  as  are  chiefly  of  scholarly  interest. 

A  large  part  of  the  experimental  data  used  in  the  book 
was  obtained  by  Professor  Gutermuth,  of  Darmstadt,  Dr. 
Stodola,  of  Zurich,  Mr,  George  Wilson,  of  Manchester,  Mr. 
Walter  Rosenhain,  of  Cambridge,  and  Professor  Rateau,  of 
Paris.  I  have  taken  the  material  from  various  sources,  and 
have  endeavored  to  give  credit  in  all  cases.  The  work  on 
nozzles  and  buckets  combined  was  done  in  the  Sibley  College 
laboratories,  and  a  series  of  similar  experiments  is  now  in 
progress  there,  in  which  the  exhaust  is  led  into  a  condenser 
maintaining  such  vacuum  conditions  as  are  used  in  practice. 

I  am  especially  indebted  to  the  officials  of  The  General 
Electric  Company,  The  W^estinghouse  Machine  Company,  The 
AUis-Chalmers  Company,  and  The  De  Laval  Steam  Turbine 
Company,  for  opportunities  for  taking  extended  observations 
at  their  works,  and  for  permission  to  use  data  and  material 
for  illustrations.  Especial  thanks  are  also  due  to  Professor 
R.  C.  Carpenter  for  placing  at  my  disposal  valuable  experi- 
mentally obtained  data;  and  to  Messrs.  A.  G.  Christie,  C.  E. 
Burgoon,  and  J.  C.  Wilson  for  assistance  in  making  calcula- 
tions and  plotting  curves. 

C.  C.  T. 

Ithaca,  N.  Y.,  January,  1906. 


PREFACE   TO   THE   THIRD   EDITION. 


In  presenting  this  third  edition  the  writer  wishes  to  call 
attention  to  the  new  problems  in  the  design  of  the  Curtis  and 
the  Parsons  types  of  turbine,  to  the  suggestions  regarding  tur- 
bine analysis,  and  to  the  Diagram  of  Heat-contents  of  Steam, 
the  superheated  region  of  which  is  plotted  from  the  results  of 
the  writer's  recent  investigation  of  the  specific  heat  of  super- 
heated steam.*  This  diagram  is  laid  out  as  suggested  by  Dr. 
Mollier,  the  co-ordinates  being  Entropy,  and  Total  Heat-contents, 
and  is  exceedingly  convenient  because  heat-units  are  read  on 
straight  lines  instead  of  on  curves  as  in  the  Temperature- 
entropy  Diagram.  The  present  edition  contains  also  new  mat- 
erial relating  to  the  application  of  steam-turbines  to  marine 
propulsion,  including  illustrations  of  some  of  the  most  recent 
turbine  steamers. 

The  object  of  the  book  is,  as  before,  to  set  forth  the  principles 
essential  to  those  who  wish  to  ec^uip  themselves  for  talking  up 
steam-turbine  work.  Only  such  details  relating  to  present 
practice  in  turbine  construction  have  been  given,  therefore,  as 
would  suffice  to  illustrate  the  application  of  the  principles. 

C.  C.  T. 

Ithaca,  N.  Y.,  November,  1907. 


*  American  Society  of  Mechanical  Engineers,  December,  1907. 


CONTENTS. 


PAGE 

Introduction ix 

CHAPTER   I. 
General    Principles   Relating    to    the    Action    of    Steam    upon 

Turbine-buckets 1 

Calculation  of  energy  of  flow.  Action  of  fluid  upon  vanes.  EfH- 
ciency  of  impulse-wheel. 

CHAPTER   II. 
Thermodynamic  Principles  Involved  in  the  Flow  of  Steam.  ...     27 
Analysis   of  energy  expenditure.     Development   of  the  funda- 
mental equations  for  flow  of  gas  and  steam. 

CHAPTER   HI. 

Graphical  Representation  of  Work  done  in  Heat  Transforma- 
tions      39 

Development  of  the  Temperature-entropy-  or  Heat-diagram. 
Examples  in  the  use  of  the  diagram. 

CHAPTER   IV. 

Calculation  of  Velocity  and  Weight  of  Flow 61 

Reaction  accompanying  acceleration  of  the  jet.  Calculations 
made  upon  the  basis  of  experimentally  determined  reaction. 

CHAPTER  V. 

Velocity  as  Affected  by  Frictional  Resistances 77 

Determination  of  energy  loss  in  the  nozzle.  Calculation  of  nozzle 
dimensions.  Experimental  determination  of  coefficient  for  friction 
losses. 

CHAPTER  VI. 
Experimental  Work  on  Flow  of  Steam  through  Orifices,  Nozzles, 

AND  Turbine-bl^ckets 93 

Calculations  of  weight  and  velocity  of  flow,  based  upon  the  re- 
sults of  experimental  work  determining  reaction  and  weight  of  flow. 

vii 


viii  CONTENTS. 

PAGE 

Experiments  with  turbine-buckets.  Effect  of  clearance.  Effect 
of  additional  sets  of  buckets.  Effect  of  cutting  over  the  edges 
of  buckets.  Effect  of  roughness  of  bucket  surfaces.  Effect  of 
back  pressure.  General  remarks  bearing  upon  the  experimental 
work  discussed. 

CHAPTER  VII. 

The   Impulse-Turbixe    151 

Single-stage, — ideal  case.  Efficiency.  Frictional  and  other 
losses.  Calculation  of  size  of  turbine.  The  two-stage  turbine. 
Velocity  diagrams.  Calculation  of  dimensions  for  given  power. 
Design  on  the  basis  of  experimentally  determined  stage  effi- 
ciency.    Specific  volume  of  superheated  steam. 

CHAPTER  VIII. 

The  Impulse-  and  Reaction-Turbine   189 

Single-stage, — ideal  case.  Many-stage, — ideal  case.  Effi- 
ciency. Calculations,  allowing  for  losses.  Characteristic  curves. 
Velocity  diagrams.  Computations  for  determining  particulars 
of  blading  and  number  of  stages.  Curve  of  frictional  effect. 
Comparison  of  efficiencies  of  the  two  types  discussed.  Heat 
analysis  of  steam-turbines.    Calorimeter  for  use  in  heat  analysis. 

CHAPTER   IX. 

Types  of  Turbine,   and   their   Operation 245 

The  De  Laval  turbine;  description  and  results  of  tests.  The 
Parsons  turbine;  description  and  results  of  tests.  Essential 
differences  between  impulse-turbines  and  reaction-turbines.  The 
compound  impulse-turbine,  Curtis  type;  general  description, 
and  results  of  tests.  Comparison  between  economy  of  turbines 
and  of  compound  reciprocating-engines.  Capacity  and  speed  of 
revolution.  Effect  of  clearance.  Effect  of  increase  of  vacuum. 
Size  of  condensers  and  auxiliaries.  Steam  used  by  auxiliaries. 
General  remarks  on  steam-turbine  design.  Note  regarding 
condensers. 

CHAPTER   X. 

The   Marine    Steam-turbine    295 

Particulars  of  vessels  equipped  with  turbines.  Reasons  for 
adopting  turbines  in  certain  classes  of  vessels.  Problems  in- 
volved. Economy  attained,  as  compared  with  reciprocating- 
engines.  Probability  as  to  more  extensive  adoption.  Cunard 
steamers  "Lusitania"  and  "Mauretania."  Appliances  for  testing 
marine  turbines. 

Appendix  320 

Examples    322 

Heat  Diagram,  or  Temperature-entropy  Chart.     Mollier  Heat 
Diagram    


INTEODUCTION. 


Rotation  in  a  steam-turbine  is  caused  by  particles  of 
steam  acting  upon  suitably  formed  surfaces  attached  to  the 
rotating  part  of  the  machine.  Steam  consists  of  very  small 
particles  or  molecules  possessing  mass,  and  the  heat  in  steam 
may  be  caused  to  impart  high  velocity  to  its  own  particles. 
This  is  accompHshed  by  allowing  the  steam  to  fall  suddenly 
in  temperature  and  thus  to  give  up  its  heat  as  work  in  expand- 
ing its  volume  and  expelling  its  own  substance  from  a  place 
of  higher  to  one  of  lower  pressure.  If  the  expansion  takes 
place  in  a  given  direction,  as  when  steam  flows  from  a  nozzle, 
the  action  is  somewhat  similar  to  that  occurring  in  the  barrel 
of  a  gun  when  the  charge  of  powder  burns,  forming  a  gas  of 
high  temperature  which  quickly  expands,  driving  before  it 
the  projectile  and  also  the  particles  of  gas  and  burnt  powder. 
The  substance  expelled  from  the  gun,  having  had  work  done 
upon  it,  attains  a  certain  velocity  and  is  capable  of  giving 
up  its  energy,  minus  certain  losses,  to  whatever  objects  may 
be  in  the  way  tending  to  retard  or  change  the  motion  of  the 
mass. 

"V\Tien  a  substance,  such  as  steam  or  water  or  gas,  flows 
through  a  nozzle  and  has  its  motion  accelerated  during  the 
flow,  a  reaction  occurs  opposite  in  direction  to  the  flow  and 
tending  to  move  the  nozzle.  The  recoil  of  a  gun  or  of  a  hose- 
nozzle  is  an  example  of  such  a  reaction.  In  turbines  of  the 
so-called  reaction  type  this  phenomenon  is  utilized  for  pro- 


INTRODUCTION. 


ducing  motion  of  the  rotating  part.  A  true  reaction-turbine 
may  be  compared  to  a  pinwheel  in  the  periphery  of  which 
small  charges  of  powder  are  exploded  and  from  which  the  result- 
ing gases  are  expelled  in  such  a  direction  as  to  give  the  wheel 
a  motion  of  rotation  due  to  the  reaction  accompanying  the 
expulsion  of  the  charge.  The  energy  possessed  by  the  charge 
leaving  the  pinwheel  might  be  directed  upon  another  movable 
wheel,  and  the  latter  be  rotated  by  the  impulse  thus  received. 
Such  a  combination  of  reaction  and  impulse  takes  place  in 


Hero's  reaction-turbine. 

what  is  called  the  reaction-turbine.  The  operation  is  as  fol- 
lows: The  stationary  casing  of  the  machine  holds  a  row  of 
guide-blades  in  front  of  each  row  of  moving  blades.  The 
space  between  each  two  guide-blades  forms  a  nozzle  through 
which  the  steam  passes  on  its  way  to  the  moving  blades.  The 
pressure  between  the  guide-blades  and  the  moving  blades  is 
less  than  that  in  the  space  before  the  guide-blades;  therefore 
the  steam  expands  as  it  passes  through  the  guide-blades,  and 
its  motion  is  accelerated  as  the  pressure  falls  during  the  expan- 
sion. The  steam  strikes  the  moving  blades  with  the  velocity 
it  has  upon  leaving  the  guide-blades,  and  exerts  an  impulse 
as  the  moving  blades  change  the  velocity  of  the  steam.  But 
there  is  a  still  lower  pressure  beyond  the  moving  blades  than 
before  them,  and  therefore  the  steam  expands  still  further  in 


INTRODUCTION. 


XI 


the  moving  blades  and  accelerates  the  velocity  of  its  own 
particles  according  to  the  amount  of  heat  given  up  during 
the  fall  of  pressure  accompanying  the  expansion.  The  moving 
blades  discharge  the  steam  in  a  direction  opposed  to  that  of 
their  rotation,  and  the  reaction  accompanying  the  accelera- 
tion of  the  steam  in  the  moving  blades  acts  to  produce  rota- 
tion, just  as  did  the  impulse  when  the  steam  first  struck  the 
moving  blades.  The  rotative  effect  is  thus  produced  by  both 
impulse  and  reaction,  and  the  name  "  reaction-turbine  "  should 
in  this  case  give  place  to  "  impulse-and-reaction  turbine." 


Branca's  impulse-turbine. 


In  an  impulse-turbine  nozzles  are  held  in  the  frame  of  the 
machine,  at  rest  relatively  to  the  earth,  and  steam  expands 
in  the  nozzles,  giving  up  its  heat  to  an  extent  depending  upon 
the  degree  of  expansion,  and  to  that  extent  does  work  upon  its 
ow^n  mass,  discharging  it  upon  the  movable  part  of  the  machine. 
The  latter  absorbs  energy  from  the  rapidly  moving  particles 
of  steam,  and  gives  out  the  energy,  minus  certain  losses,  as 
rotative  effort.  The  steam  particles  receive  in  the  nozzles 
all  the  mechanical  energy  they  are  to  possess,  for  there  is  in 
the  ideal,  single-stage  impulse-turbine  no  fall  in  pressure  after 
the  steam  leaves  the  nozzles.  There  is  therefore  the  same 
pressure  on  the  two  sides  of  the  rotating  row  of  blades,  and 
the  latter  simply  receive  an  impulse  due  to  the  reduction  in 
kinetic  energy  which  the  steam  experiences  during  its  passage 
through  the  blades. 

In  the  many-stage  impulse-turbine  the  fall  in  pressure  and 


xii  INTRODUCTION. 

temperature  occurring  in  any  one  stage  is  limited  according 
to  the  work  that  is  desired  to  be  produced  by  a  single  stage. 
Thus  the  steam  still  possesses  energy  after  its  passage  through 
the  blades  in  a  given  stage,  and  this  remaining  energy  may 
be  used  in  a  succeeding  stage  in  the  manner  described.  The 
smaller  the  amount  of  energy  remaining  in  the  steam  after 
passage  through  the  final  stage  of  the  turbine,  the  more  effi- 
cient is  the  machine  as  a  heat-engine. 

In  general,  steam-turbine  design  is  concerned  primarily 
with  the  use  of  the  energy  of  rapidly  moving  masses  of  steam 
and  with  the  heat  transformations  which  give  rise  to  the  motion 
of  the  steam.  A  knowledge  of  the  principles  underlying  these 
phenomena  is  therefore  necessary,  and  the  first  three  chapters 
were  written  to  make  the  fundamentals  clear.  In  Chapters  IV, 
V,  and  VI,  the  flow  of  steam  through  orifices  and  nozzles  is 
discussed,  and  experimentally  obtained  results  are  given  in 
order  to  connect  what  would  be  expected  to  occur  under  ideal 
conditions  with  what  actually  occurs  in  engineering  practice. 

In  the  remaining  chapters  the  principles  of  turbine  design 
and  operation  are  discussed,  and  it  has  been  the  constant 
aim  in  this  work  to  show  in  what  way  the  results  to  be  expected 
may  be  predicted  by  the  proper  use  of  experimental  data. 


CLASSIFICATION  OF  STEAM-TURBINES. 


1.  Impulse   turbines, 
buckets. 

Reaction,  or 
Impulse-  and-re- 
action  turbines. 


Equal  pressure  on  the  two  sides  of  any  row  ot 


Impulse 
type. 

Partial 
peripheral 
admission, 
excepting 
Hamilton- 
Holzwarth. 


Nozzles 

inclined 

to 

Plane 

of 
Rota- 
tion. 


}•  Fall  of  pressure  in  passing  anv  row  of  buckets. 

J 

(a)  Single  stage,  consisting  of  one  set  of  nozzles 
and  one  row,  or  wheel,  of  buckets.  (Ex- 
ample, De  Laval  turbine.) 

(h)  Velocity  compounded,  single  stage,  one  set  of 
nozzles  and  several  rows  of  moving  buckets, 
with  intermediate  guides.     (Curtis  ) 

(r)  Pressure  Compounded,  several  compartments, 
or  stages,  each  containing  one  set  of  nozzles 
and  one  set  of  moving  buckets.  (Rateau, 
Zoelly,  Hamilton-Holzwarth.) 

((/)  Several  stages ;  both  pressure  and  velocity  com- 
poundel.  Each  compartment,  or  stage, 
contains  one  set,  (perhaps  divided  into  two 
groups)  of  nozzles,  and  two  or  more  rows  of 
moving  buckets,  and  one  or  more  rows  of 
stationary  buckets.  (Curtis,  vertical  and 
horizontal.) 

(e)  One  or  more  stages.  Buckets  of  Pelton  tj-pa 
cut  in  rim  of  wheel.  Nozzles  in  plane  of 
rotation.     (Riedler-Stumpf.) 


Full  peripheral  admis-  /  Many  stage  turbine,  or  Parsons  type, 
sion.  I  by  both  impulse  and  reaction. 


Steam  acts 


Partial  peripheral  ad- 
mission in  Impulse 
stages,  and  full  peri- 
pheral admission  in 
Parsons  stages. 


Combinaton  of  Impulse  stages  with  those  of  the 
Impulse-and-reaction  type.  Generally  one 
or  more  Impulse  stages  at  high  pressure  end 
of  turbine,  followed  by  a  large  number  of 
Impulse-and-reaction,  or  Parsons  stages. 

xiii 


STEAM-TURBINES. 


CHAPTER  I. 

GENERAL  PRIXCIPLES  RELATING  TO  THE   ACTION   OF  STEAM 
UPON   TURBINE-BUCKETS. 

The  effect  of  steam  striking  against  and  lea\ing  the  mo^^ng 
parts  of  a  turbine  may  be  analyzed  by  means  of  the  principles 
discussed  in  the  present  chapter. 

A  force  acting  upon  a  body  tends  to  change  the  position  of 
the  body.  If  the  latter  is  at  rest  relatively  to  the  earth,  it  is 
said  to  have  zero  velocity,  and  a  force  may  act  so  as  to  impart 
to  the  body  a  certain  motion.  If  the  body  is  in  motion  before 
the  force  acts  upon  it,  the  effect  of  the  force  is  to  increase  or 
decrease  the  rate  of  motion  of  the  body,  or  else  to  change  its 
direction  of  motion.  Or,  the  force  may  change  both  the  rate 
and  the  direction  of  motion.  Change  of  rate  of  motion  is 
called  acceleration.  If  a  force  increases  the  velocit}'  of  a  bodv, 
it  is  said  to  produce  a  positive  acceleration.  If  the  effect  of  the 
force  is  to  reduce  the  velocity,  it  is  said  to  produce  a  negative 
acceleration. 

If  the  mass  of  a  body  be  known,  and  the  acceleration  in  a 
given  direction  due  to  a  force  be  also  known,  the  magnitude 
of  the  force  can  be  calculated.  It  follows,  therefore,  that  a 
force  can  be  measured  by  the  acceleration  it  produces  when 
it  acts  upon  definite  quantities  of  matter  whose  conditions  of 


2  STEAM-TURBINES. 

motion  are  known.  If  a  force  communicates  equal  increments 
of  velocity  in  equal  lengths  of  time,  it  is  said  to  be  a  uniform 
force. 

If  a  force  acts  upon  a  body  in  a  fixed  direction,  and 
produces  an  acceleration  /, — that  is,  if  it  adds  /  units  of  velocity 
per  unit  of  time, — then  in  t  units  of  time  the  velocity  generated 
isF  =  //. 

The  space  passed  over  in  the  time  t  is  the  product  of  the 

V 
mean  velocity  ^  and  the  time  t. 

If  space  passed  over  is  s,  then 

sJlxt  =  ift^ 

V  72     72 

But  t = -J,  and  therefore    s  =  J/  X -7^  ^2f' 

This  may  be  written       V^  =  2/s. 

Applying  this  general  statement  to  the  case  of  a  body  falling 
freely  towards  the  earth,  under  the  influence  of  the  force  of 
gravitation,  whose  acceleration  is  called  g,  the  space  through 
which  the  body  must  fall  in  order  that  it  may  attain  the  velocity 

72 
V,ish  =  ^. 

If  a  free  body  of  mass  M  is  acted  upon  by  a  force  F, 
in  a  fixed  direction  during  a  given  time,  a  certain  acceleration 
of  the  motion  of  the  body  will  take  place.  If  the  force  F  acts 
upon  a  mass  of  2M  during  the  same  length  of  time,  the  accelera- 
tion, or  increase  of  velocity,  will  be  only  half  as  great  as  in 
the  first  instance.  To  produce  the  same  effect  in  the  same 
time  upon  2M  as  was  produced  by  F  upon  M,  the  force  must 
be  27^. 

Further,  if  a  force  F  produces  an  increase  of  velocity,  V, 
in  a  mass  M  in  a  p;iven  time,  it  will  require,  a  force  of  2F  to 
produce  a  velocity  of  2V  in  the  same  mass  in  the  same  time. 


ACTION  OF  STEAM   UPON  TURBINE-BUCKETS.  3 

And  if  a  certain  force  imparts  in  one  second  to  a  mass  weigh- 
ing 2  pounds  a  velocity  of  2  feet  per  second,  it  is  capable  of 
imparting  to  a  mass  of  4  pounds  a  velocity  of  only  1  foot  per 
second. 

From  these  facts  it  is  seen  that  the  force  required  to  change 
the  motion  of  matter  varies  as  the  acceleration,  or  velocity 
acquired  in  a  given  time,  and  as  the  mass  acted  upon.  It 
therefore  varies  as  their  product,  and  since  a  force  F,  which 
accelerates  the  velocity  of  a  mass  ^1/  by  an  amount  /  per 
unit  of  time,  varies  as  the  product  Mf,  the  equation  may  be 
written  F  =  CMf,  where  C  is  some  constant. 

The  imit  of  mass,  as  used  in  engineering,  is  a  derived  unit, 
and  its  value  may  be  found  in  terms  of  force  and  acceleration  by 
letting C=l.  The  earth  attracts  every  mass  of  matter  upon  its 
surface  "^dth  a  force  (called  the  force  of  gra^dtation)  capable 
of  imparting  to  the  mass  an  acceleration  of  about  32.2  feet 
per  second  per  second.  The  magnitude  of  the  force  is  pro- 
portional to  the  amount  of  matter,  or  the  mass,  acted  upon, 
and  is  called  the  weight  of  the  mass.  The  weight  of  a  certain 
mass  of  platinimi  has  been  accepted  as  the  unit  force,  and 
is  called  the  pound.  If  F  =  l  pound  and  /  =  32.2  feet  per 
second  per  second,  the  equation  may  be  written: 

^^  =  M  =  the  amount  of  mass  in  1  pound  weight. 

The  value  of  M  in  this  equation  can  be  made  equal  to 
unity  only  by  multiplying  the  left-hand  member  by  32.2, 
and  therefore  the  unit  mass  is  so  much  mass  as  weiglis  32.2 
lbs.  To  express  quantities  of  mass,  then,  in  terms  of  weight, 
it  is  necessary  to  di^^de  the  weight  of  the  mass  by  32.2,  or 
M  =  W -^32.2.  Calling  the  acceleration  due  to  gra\'ity  g,  the 
equation  becomes 

The  equation  expressing  the  relation  between  force,  mass, 
and  acceleration  is,  then, 

W 


4  STEAM-TURBINES. 

W 
where  F  is  the  force  which  produces  in  the  mass  —  the  accel- 
eration /. 

A  weight  W,  if  allowed  to  fall,  is  accelerated  by  an  amount 
g  ft.  per  second.  Forces  are  proportional  to  the  acceleration 
they  produce  upon  bodies  free  to  move,  and,  therefore,  any 
force  F  which  can  produce  an  acceleration  /  is  related  to  W 

F     W 
and  g  by  the  equation  y  = — .     Hence  the  force  i^  which  can 

give  a  velocity  of  /  ft.  per  second  to  a  mass  TF,  in  1  second, 

Wj 
IS  equal  to  — =Mf,  where  ilf  =  the  mass  accelerated. 

If  a  stream  of  any  substance,  such  as  water,  gas,  or  steam^ 
or  of  a  mixture  of  steam  and  water,  moves  with  a  velocity  Vy 
in  a  fixed  direction,  then  if  W  is  the  weight  of  the  substance 
passing  a  given  cross-section  of  the  conducting  channel  per 
second,  the  work  it  is  capable  of  doing,  or  the  energy  it  possesses 
by  reason  of  its  mass  and  velocity,  is  the  same  as  the  energy 
developed  by  a  body  falling  freely  under  the  action  of  gravity 
through  a  height  h,  and  thereby  acquiring  the  velocity  V. 

If  K  be  the  kinetic  energy  of  the  stream,  or  its  capacity 

Tf72 
to  do  work,  then  /^-TF/i--^ — (2) 

Hence  the  energy  of  a  stream  of  constant  cross-section  is 
proportional  to  the  square  of  its  velocity. 

If  a  nozzle  delivers  W  pounds  of  the  substance  per  sec- 
ond with  a  uniform  velocity  V,  it  may  be  considered  that  a 
constant  impulsive  force  F  has  acted  upon  the  weight  W  for 
one  second  and  then  ceased.  During  this  second  the  substance 
has  changed  its  velocity  from  0  to  V,  and  has  traversed  the- 

space  W'    Therefore  the  work  Fx-^  has  been  done  upon  the 

substance  by  the  impulsive  force  F. 

The  energy  of  the  jet  is  -^ — ,  and  this  must  equal  the  work 

V 

which  has  been  done  upon  the  jet,  or  -^X^- 


ACTION  OF  STEAM   UPON   TURBINE-BUCKETS.  5 

Hence  FXi^=-^^-,     or    F  =— (3) 


V    WV^  ^    WV 

Fx^=-^r-,     or    F  = . 

2       2^'  g 


If  A  =  th.e  area  of  cross-section  of  the  jet,  and  the  weight  of 
the  substance  per  cubic  umt  =  w,  then  W  =  wAV,  or 


F  = 


wAV^ 
9 


The  jet  is  capable  of  exerting  an  impulse  equal  to  F  upon 
any  object  in  its  way,  and  therefore  the  impulse  of  a  jet  of 
constant  cross-section  varies  as  the  square  of  its  velocity. 

The  force  F  acts  for  one  second  upon  each  W  pounds  of 
substance  which  pass  a  given  section.  But  as  there  is  only  the 
amount  W  passing  per  second,  the  force  F  is  continuously 
exerted  and  becomes  a  continuous  impulsive  pressure. 


Fig.  1. 

A  stream  flowing  from  an  orifice  produces  a  reaction 
equal  in  value,  and  opposite  in  direction,  to  the  impulse  the 
stream  is  capable  of  producing  upon  an  object  against  which 
it  may  strike.  In  the  direction  of  the  jet  the  impulse  produces 
motion.  In  the  opposite  direction  it  produces  a  pressure 
tending  to  move  the  orifice  or  nozzle  and  whatever  is  rigidly 
connected  therewith. 


The  force  i^  = 


WV    wAV^ 


is  exerted  in  the  line  of  action  of 


6  STEAM-TURBINES. 

the  jet,  and  its  force  in  any  other  direction  is  the  component  of 
the  force  F  in  that  direction. 

If  steam,  for  example,  issues  vertically  downward  from  an 
orifice  in  the  base  of  a  vessel,  it  exerts  an  upward  reaction  F 
and  a  horizontal  reaction  0.  If  its  direction  of  issue  is  inchned 
20°  to  the  vertical,  its  upward  reaction  is  F  cos  20°,  and  its 
horizontal  reaction  is  F  sin  20°.     (Fig  1.) 

If  a  stream  moving  with  velocity  Vi  is  retarded  so  that 

its  velocity  becomes  V2,  its  impulse  at  first  is  W —  and  after 

Vo 

retardation  TF— ".    The  dynamic  pressure  developed  is 


9 

It  is  by  means  of  the  pressure  resulting  from  change  of  velocity 
or  of  direction  of  flow,  or  both,  that  turbine-wheels  transform 
the  energy  of  moving  water,  steam,  or  gas  into  useful  work. 

Example  1 . — 200  pounds  of  water  flows  each  second  from  an 
orifice  having  a  cross-sectional  area  of  .064  sq.  ft.  What  is  the 
velocity  of  flow? 

Quantity  =  area  X  velocity,  or 

200-^62.4  =  3.2  cu.  ft.  per  second. 
3.2^0.064  =  50  ft.  per  second. 

What  is  the  horse-power  of  the  jet? 
Energy,  or  capacity  to  do  work, 

WV^     200.  X  (50.)2 
=  ~^ — = ^jT =  7760.  ft.-pds.  per  second. 

7760.  H-550.  =  14.1  horse-power. 

What  is  the  reaction  against  the  vessel  from  which  the 
water  flows? 

■x>      ,-        ■        ^        T?    ^^    200X50    ^^^  , 

Reaction = impulse =i'  = =    ^o  o    ==311  pounds. 


ACTION  OF  STEAM    UPON   TURBINE-BUCKETS.  7 

If  the  water  should  act  upon  a  revolving  wheel,  leaving  the 
buckets  at  a  velocity  of  30  ft.  per  second,  what  horse-power 
would  be  given  up  to  the  wheel?    Neglect  losses. 

WiVi^-Vi")     200((50)2-(30)2) 
Energy  given  up  = -^ = ^^ 

=  4960  ft.-pds.  per  second. 
4960  ^  550  =  9 .04  horse-power. 

Efhciency  of  wheel,  disregarding  friction,  =9.04-^14.1  =  .64. 

If  the  water  at  30  ft.  per  second  should  be  used  to  drive 

another  wheel,  leaving  its  buckets  at  a  velocity  of  10  ft.  per 

second,  what  would  be  the  efficiency  of  the  two  wheels  combined? 

TT  f  1     1.    1     200  X  ((30)2 -(10)2) 

Horse-power  oi  second  wheel  = jtt—a — j^p^ =  4.52 

^  64.4x550 

"  "  first  "  =  9.04 


*'  "  two  wheels  =13.56 

Efficiency  =  13.56 -^  14.1  =  .96 +  . 

The  same  total  efficiency  would  of  course  be  obtained  by 
using  the  first  single  wheel,  if  the  water  should  leave  it  at 
the  velocity  of  10  ft.  per  second. 

^,  200((50)2-(10)2) 

Ihus,       a4  A  wrrn —  =  13.5  +  horse-power. 

'  64.4x550  ^ 

13.5  -^  14.1  =  .96,  approximately. 
The  efficiency  of  the  system  of  wheels  is  evidently 
7i2-Fo2    2500-100 


7i2  2500 


=  .96. 


Example  2. — Suppose  100  pds.  steam  to  flow  per  second  from 
the  orifice  of  the  previous  example,  what  would  be  the  horse- 
power of  the  jet? 


8  STEAM-TURBINES. 

The  area  of  the  orifice  is  .064  sq.  ft.  (about  3.4  ins.  diam.). 
Let  the  volume  of  steam  per  pound=2.5  cu.  ft.  in  the  orifice. 

100x2.5 

-      „  „  . '   =  3900  ft.  per  second  velocity. 

.     ,      ,  .            ,        WV^     100  X  (3900)2 
Energy,  or  capacity  tor  domg  work,  =  -^ —  = nj^ ■  = 

23,600,000  ft.-pds.  per  second. 
23,600,000 


550 


=  42,900  horse-power. 


If  the  steam  in  such  a  jet  should  all  be  used  upon  a  tur- 
bine, leaving  same  at  a  velocity  of  1000  ft.  per  second,  what 
horse-power  would  be  developed,  disregarding  frictional  and 
thermal  losses? 

W(V,2-V2^)      100((3900)2- (1000)2) 
Energy  given  up ^^ = ^^ 

=  22,200,000  ft.-pds.  per  second. 
22,200,000 


550 


40,400  horse-power. 


40,400      ^, 
Efficiency^  42900^ 

What  would  be  the  reaction  against  a  steam-nozzle  from 
which  such  a  stream  was  emitted? 

^     WV     100X3900     ^....  , 

F= =  — ^?r^, —  =12,100  pounds. 

9  '^2.2 

Example  3. — If  a  jet  has  a  cross-sectional  area  of  1  sq. 
inch,  how  many  cubic  feet  of  air  at  atmospheric  pressure  must 
it  emit  per  second  in  order  that  its  impulse  may  be  200  pounds? 

1  cu.  ft.  of  air  at  atmospheric  pressure  and  60  degrees  F. 
weighs  approximately  1/13  pound. 


ACTION  OF  STEAM    UPOX   TURBINE-BUCKETS.  9 

If  ir  =  weight  of  air  per  cu.  ft.  and  A  =  area  of  orifice  in 
sq.  ft.,  then 


^    WV    2wAV2    wAV^     ^^^ 

F= =  — ^ —  = =  200  pounds. 

g        ^g         g  ^ 


1       1       F2 
13><l44X32:2=200,     or 


V  =  V2OO.  X  32.2  X 144.  X 13.  =  3490.  ft.  per  second. 
3490. 


144. 


24.  cu.  ft.  per  second. 


Example  4- — If  a  tube  T  is  1"  dia.  and  deUvers  0.3  cu.  ft. 
of  water  per  sec.  compute  the  dynamic  pres,  against  the  plane. 


785 
A=j^  .?q.  ft.     Tr  =  .3  cu.  ft.  =  18.7  pds. 


^^     .3X144 

V  =- — -or    =00  it.  per  sec. 


WV    18.7X55 


F^  —  =     g^^     =  32  pds.,  approx. 


Fig.  2. 


Example  5. — If  a  nozzle  having  a  cross-sectional  area  of 
0.1  sq.  in.  discharges  500  pounds  of  steam  per  hour,  and  expedi- 
ences a  reaction  against  itself  of  15  pounds,  what  is  the  velocity 
of  the  issuing  jet  of  steam? 


10 


STEAM-TURBINES. 


Since  the  reaction  is  equal  to  the  impulse  the  jet  is  capable 
of  exerting,  it  equals 

„     WV  ^,    Rg     15X32.2     ^,^^  ,^ 

R  =  —,     or     V  =  -^=      ^QQ      =3480  ft.  per  sec. 

3600 

Action  of  Fluid  upon  Vanes. — Let  a  stream  of  fluid  enter  a 
stationary  vane  tangentially  to  the  surface  at  A,  Fig.  3,  and  let 


(lY 


Fig.  3. 


it  traverse  the  vane  to  B  with  the  velocity  it  had  at  A.  This 
condition  would  be  possible  if  the  fluid  experienced  no  frictional 
resistance  to  its  passage  along  the  surface.  As  the  fluid  enters 
the  vane  its  tendency  is  to  continue  flowing  in  the  direction  it  has 
at  A,  but  it  is  prevented  from  maintaining  this  direction  of  flow 
by  the  curvature  of  the  surface  it  has  to  traverse.  The  vane 
has  to  oppose  a  resistance  to  the  tendency  of  the  fluid  to  flow 
in  its  original  direction,  in  order  to  effect  the  change  in  direc- 
tion, and  that  resistance  amounts  to  a  force  pushing  the  fluid 
towards  the  center  of  curvature  of  the  vane  at  each  point 


ACTION  OF  STEAM   UPON   TURBINE-BUCKETS.  H 

of  the  path.  The  force  causing  the  stream  to  take  the  direc- 
tion of  the  vane  surface  is  similar  to  the  pull  on  a  string  by 
which  a  weight  is  held  and  caused  to  swing  about  the  point 
at  which  the  string  is  held.  If  a  certain  weight  of  fluid,  for 
the  instant  in  which  it  covers  the  distance  dl,  is  rotating  about 
a  center  at  C,  it  is  exerting  a  pressure  in  a  direction  normal 
to  the  surface  at  dl,  and  that  pressure  is  equal  in  amount  to 
the  centrifugal  force  exerted  by  a  body  having  the  same  weight 
as  the  v/ater  on  dl,  and  moving  with  the  velocity  F  at  a  distance 

r  from  the  center  of   rotation.     The  centrifugal  force  = , 

or,  if  the  area  of  cross-section  of  the  stream  is  A  sq.  ft.  and 
the  fluid  weighs  w  pounds  per  cubic  foot,  the  weight  W=Awdl 
and  the  centrifugal  force  on  dl  is 


^„    Adlw     72 

dP= X— . 

9         r 


The  pressure  on  the  small  area  of  length  dl  in  the  direction 
which  the  stream  had  when  it  entered  the  vane  is 

dX=dP  sin  a, 

and  in  the  direction  perpendicular  to  that  of  the  stream  at 
entrance  it  is  dY  =  dP  cos  a. 

The  total  angle  subtended  by  the  surface  of  the  vane  is  /?^ 
and  upon  each  elementary  area  of  width  dl  there  is  the  force 
dP  pressing  against  the  vane.  The  total  component  of  the 
force  in  the  direction  of  dX  is 


Px=  dX=  /       dPsina 

2    r^dlsma 
Jo        r 


AwV^   r^dl  sin  a 


12  STEAM-TURBINES. 

But  dl=rda,  and  therefore 


■2    r? 
Jo   "^^ 


Fx  = •  /    sin  ada 

9 


■■ (l-cos/5). 


r^  AwV^ 

Similarly,      Py'^  /    dP  cos  a  = sin  /9. 

Jo  9 

The  resultant  impulse  on  the  vane  is 

Ayriy2     

Pr  =V'Px^+Py^  = \/2(l  -cos  /?). 


Since  the  volume  of  fluid  passing  the  surface  per  second 
is  equal  to  the  cross-sectional  area  of  the  stream  multiplied 
by  the  velocity,  and  since  the  volume  multiplied  by  the  weight 
per  cubic  unit  equals  the  total  weight  flowing  per  second, 

Weight  flowing  per  second  =  TF  =  w;AF. 

The  expressions  for  impulse  may  then  be  written  as  follows: 

WV 
Px-— (1-cos/?); (4) 

Py= sm^;       (5) 


Pfi  =  — V2(l-cos/?) (6) 


The  direction  of  Pr  with  respect  to  Px  and  Py  is  given 
by  the  equation 

Py       sin  /? 

cot  «  =  B~  =  1 1,' 

Fx     1  — cos/3 


ACTION  OF  STEAM   UPON   TURBINE-BUCKETS. 


13 


The  matter  may  be  approached  by  a  method  more  direct, 
though  less  satisfactory  from  an  analytical  standpoint,  as 
follows:  If  a  stream  of  constant  cross-sectional  area  flows 
with  a  constant  velocity  V  and  is  deflected  by  the  surface  of 
a  vane,'  as  in  Fig.  4,  the  impulse  it  is  capable  of  producing 
in  the  direction  of  flow  is  the  same  at  all  points  of  the  path. 
The  reaction  exerted  by  the  stream  in  the  direction  opposite 
to  that  of  flow  is  also  constant.    As  the  stream  enters  the 


Fig.  4. 

surface  it  exerts  its  impulse  R  in  the  direction  of  flow,  and 
as  it  leaves  the  surface  the  reaction  R  is  exerted  in  a  direction 
opposite  to  that  of  flow. 

Let  P  be  the  dynamic  pressure,  or  the  impulse  produced  in 
the  direction  of  the  initial  motion  as  the  jet  strikes  the  vane, 
and  let  Ri  be  the  component  in  that  direction  of  the  reaction 
of  the  jet  as  it  leaves  the  vane.  Then,  if  /?  is  greater  than 
90°,  as  shown  in  Fig.  4,  the  total  pressure  upon  the  vane  is 

P  =  R  +  Ri=R  +  R  cos  (180° -^)=R{l-cos  13). 
If  /?  is  less  than  90°, 

P  =  R-Ri=R-R  cos  l3==R{l-cos^), 


14 


STEA  M-  T  URBINES. 


The  result  is  the  same  in  the  two  cases,  and  the  value  of 

the  impulse  is  seen  to  depend  upon  the  angle  of  exit  of  the 

WV 
vane.    Since  the  impulse  R  = ,   the   total  pressure  is,   as 


before  found, 


WV 

P= (1-cos/?). 

9 


If  /?  =  0,  as  when  a  stream  flows  along  a  straight  surface, 
P  =  0. 

WV 
If/9  =  90°,  as  in  Fig.  5,  cos/?  =  OandP  = . 


//^/////////////////////^^. 


^m 


V 


z. 


Fig.  5. 

/////////////yy/////////////. 


Fig.  6. 


If  /?  =  180°,  as  in  Fig.  6,  a  complete  reversal  of  direction 
occurs,  and 

WV 


ACTION  OF  STEAM   UPON   TURBINE-BUCKETS. 


15 


If  the  direction  in  which  it  is  required  to  find  the  dynamic 
pressure  makes  an  angle  a  with  the  direction  of  the  entering 
jet,  and  an  angle  ^5  with  that  of  the  jet  when  it  leaves  the  vane. 


Fig.  7. 

the  components  of  the  impulsive  pressure  in  the  direction  of 
Pi  and  P2,  Fig.  7,  are 

Pi  =72  cos  a, 

WV 

P  =  R(cos  a  +COS  /?)  = (cos  a  +  cos  /?). 

If  a  =  0°  and  .9  =  90°,  as  in  Fig.  5,  then  P  =  R. 

If  a:=0  and  /3=0,  as  in  Fig.  6,  then  P  =  2R. 

Let  a  vane,  or  "  bucket,"  move  with  velocity  u,  in  a  straight 
line,  when  acted  upon  by  a  jet  of  fluid  having  a  velocity  V  in 
the  same  direction  as  the  motion  of  the  vane. 


16 


STEAM-TURBINES. 


Let  the  stream  at  exit  from  the  vane  have  a  direction  mak- 
ing an  angle  /?  with  a  hne  drawn  in  direction  opposite  to  that 
of  the  velocity  u.  The  velocity  of  the  jet  relatively  to  the 
vane  is  V —  u,  and  a  dynamic  pressure  is  produced  upon  the 
vane  in  the  direction  of  motion,  just  as  if  the  vane  were  at  rest 


//////////////////. 


Fig.  8. 

and  were  acted  upon  by  a  jet  moving  with  the  absolute  velocity 
Y-u. 

For  a  surface  at  rest  the  action  of  a  jet  having  a  velocity 
F  produces  a  pressure  in  the  direction  of  the  jet's  motion  of 


P  =  (l+cos/?) 


WY 


ACTION  OF  STEAM   UPON   TURBINE-BUCKETS  17 

where  /?  is  the  angle  between  the  directions  of  the  jet  when 
entering  and  leaving  the  vane.  For  the  surface  in  motion, 
F  — w  is  to  be  substituted  for  V  and  the  equation  becomes 

g 

The  weight  of  fluid,  W  pounds  per  second,  is  supposed  to 
all  act  upon  the  vane. 

At  the  point  of  exit  of  the  jet  from  the  vane,  Fig.  8,  lines 
may  be  drawn  representing  u  and  V —  u  in  magnitude  and 
direction.  The  diagonal  Vi  represents  in  magnitude  and 
direction  the  absolute  velocity  of  the  jet  as  it  leaves  the  vane. 

The  impulse  of  the  jet  as  it  enters  the  vane,  in  the  cUrec- 

WV 
tion  of  motion  of  the  vane,  is ;   and  as  it  leaves  the  vane 

g 

,         .  ,  .       WVl  COS  i    .  ,  T  •  m,  ,.  , 

the  impulse  is  — — in  the  same  direction.    Therefore  the 

g 

pressure  in  the  direction  of  motion  of  the  vane  is 

W 

P=— (7-7icos  J). 

g 

But  Vi  cos  A=u~{V —u)  cos  /?,  and  therefore 

When  /9  =  180°  there  is  no  pressure  exerted  upon  the  vane, 
and  the  pressure  becomes  a  maximum  when  ,'3  =  0,  for  this 
causes  a  complete  reversal  of  the  direction  of  motion  of  the  jet. 

When  the  jet  strikes  the  vane  as  in  Fig.  9,  at  an  angle  a 
with  the  direction  of  motion  of  the  vane,  the  stream  traverses 
the  surface  of  the  vane  with  a  relative  velocity  v,  found  by 
combining  u  and  Fi,  and  finding  their  component  along  the 
surface  of  the  vane  at  entrance.    The  velocity  upon  leaving 


18 


STEAM-TURBINES. 


the  vane  is  also  v,  shown  making  an  angle  /5  with  the  direction 
of  motion  of  the  vane.  The  absolute  velocity  of  the  jet  as  it 
leaves  the  vane  is  Fa. 


Fig.  9. 

The  impulse  with  which  the  jet  strikes  the  vane  is -'  and 

WVi 
its  component  in  the  direction  of  motion  of  the  vane  is cos  a, 

WVo 
As  the  jet  leaves  the  vane  the  impulse  is and  its  component 

.    WVo 

in  the  direction  of  motion  of  the  vane  is cos  J. 

9 
The  total  impulse  in  the  direction  of  motion  of  the  vane  is 

W 

P= — (Yi  cos  a  — F2  cos  J). 

9 

Example  6.— Let  a  =  30°.     ^  =  40°. 

Let  Fi=3000  ft.  per  sec.  and  w  =  1000  ft.  per  sec.    Then 

F2  cos  i  =  w  —  V  cos /?, 


ACTION  OF  STEAM    UPON   TURBINE-BUCKETS.  19 

and 

W 
P= — (Fi  cos  a—u  +  y  cos/?). 

The  value  of  v  may  be  found  from  the  lower  velocity  diagram; 

thus 

V  =\/u~  +  V{^  —  2uVi  cos  a 


=\/(1000)2  + (3000)2- 6,000,000 X. 866  =  2192  ft.  per  sec. 
P=  (3000  X  .866  - 1000  +  2192  X  .766)-21  =  lOOTF,  approx. 


If  T7  =  1  pound  per  second,  then  the  impulse  produced  upon  the 
vane  is  100  pounds. 

The  direction  of  the  Hne  representing  the  velocity  of  the 
steam  relatively  to  the  vanes  or  blades  of  a  turbine  should  be 
such  that  the  stream  or  jet  enters  the  blade  tangentially  to 
its  working  face.  Otherwise  losses  due  to  impact  and  friction 
will  be  greater  than  necessary. 

Note. — The  difference  between  the  meanings  of  impact  and 
impulse  should  be  noted.  Impact  results  in  loss  due  to  friction 
between  the  particles  of  fluid  themselves,  or  between  the  fluid 
and  some  ol^ject  upon  which  it  impinges.  Impulse  refers  to  the 
dynamic  pressure  exerted  upon  some  object,  as  a  vane,  by  a 
jet  possessing  kinetic  energy.  The  term  impact-wheel  is  there- 
fore a  misnomer  when  applied  to  turbines  used  for  obtaining 
useful  transformations  of  energy. 

If  the  jet  is  to  enter  the  blade  tangentially  to  its  surface, 
the  curve  of  the  blade  at  the  edge  where  the  jet  enters  should 
be  tangent  to  the  line  of  relative  velocity  v. 

If  the  angle  a  is  given,  y,  Fig.  9,  may  be  found  from  the 
equation 

sin  {x—a)      u 
sin  Y      ~  Vi 


20  STEAM-TURBINES 

from  which 

cot  ^  =  cot  a  — 


Fi  sin  a 


Thus  the  proper  value  of ;-,  the  angle  of  the  blade  at  the  entering 
edge,  can  be  found  when  u,  Vi,  and  a  are  given. 

Work  Done  by  the  Fluid  Acting  against  the  Vane  or  Bucket. 
Neglecting  leakage  past  the  blades  of  a  turbine,  all  the  steam 
passing  through  it  acts  to  produce  rotation.  If  the  steam 
enters  in  the  direction  of  motion  of  the  blades  (the  latter  is  not 
the  case  in  most  steam-turbines),  leaving  at  an  angle ^  with 
the  direction  of  motion,  the  pressure  resulting  in  the  direction 
of  motion  is 

W 

The  velocity  of  the  blades  being  u,  the  work  done  per  second  is 
Pu=(\  (1+cos/?)— (7i-w) 

If  11  is  zero,  the  work  becomes  zero,  while  it  becomes  a  maximum 

y 
when  u=-^,  or  when  the  linear  velocity  of  the  blades  is  half 

that  of  the  jet.     Making  u  =  -^   m  the  above  equation,   the 

work  done  at  the  wheel  =  (l +cos/?)TF-j-. 

Dividing  by  the  energy  of  the  jet,  ^^-^,  the  efficiency  of 

the  jet  is 

1  +  cos^ 

Assuming  the  jet  to  enter  the  blades  as  stated  above,   the 
efficiency  is  seen  to  depend  entirely  upon  /?,  the  angle  of  exit 


ACTION  OF  STEAM   UPON   TURBINE-BUCKETS.  21 

from  the  blades.     When  /?  =  180°,  ^  =  0;  when  /?  =  90°,  £"  =  .5; 
and  when/?  =  0°,  ^  =  1. 

In  general,  the  efficiency  of  a  turbine  depends  upon  the 
relation  between  the  speed  of  blade  and  that  of  the  entering 
jet  of  fluid,  of  whatever  kind  the  latter  may  be.  Assuming 
that  entrance  and  exit  angles  are  favorable,  the  highest  effi- 
ciency may  be  expected  when  the  speed  of  blade  is  from  one 
third  to  one  half  the  speed  of  the  entering  jet.  This  ratio  for 
highest  efficiency,  however,  depends  upon  the  action  of  the 
fluid,  whether  it  works  by  impulse  alone,  or  by  reaction  alone^ 
or  by  both. 

Referring  to  Fig.  10  on  page  22,  let  AB  represent  in  magni- 
tude and  direction  the  absolute  velocity,  or  the  velocity  rela- 
tively to  the  earth,  of  the  entering  steam.  Let  CB  represent 
the  peripheral  velocity  of  the  vanes  or  blades  of  the  turbine. 
Then  AC  will  represent  the  velocity  of  the  entering  steam 
relatively  to  the  blades,  and  J  will  be  the  proper  blade  angle. 
If  the  blade  curve  makes  this  angle  with  the  direction  of  motion 
of  the  blade,  no  shock  will  be  experienced  when  the  steam 
enters  the  blade.  Let  the  angle  at  which  the  steam  leaves  the 
blade  be  j3.  Then  the  absolute  velocity  of  the  departing  steam 
is  represented  by  CE. 

A  blade  may  be  sketched  in  at  C,  Fig.  10,  making  angles  J 
and  /?  with  the  direction  of  motion  of  the  blade,  and  for  given 
values  of  a  and  /?,  and  for  a  known  weight  of  steam  flowing  per 
second,  and  a  known  peripheral  velocity  of  blade,  the  pressure 
on  the  blade  can  be  computed  as  was  done  in  Example  6. 

For  the  compounded  turbine  the  same  method  may  be 
extended,  as  shown  in  Fig.  11.  AB  and  NP  represent  respect- 
ively the  initial  and  final  absolute  velocities  of  the  steam,  and 
the  energy  given  up  by  the  steam  will  be  proportional  to  the 
difference  of  their  squares.  Further  discussion  of  this  arrange- 
ment will  be  given  later. 

The  preceding  discussion  illustrates  the  method  by  which 
problems  concerning  the  action  of  jets  upon  turbine  vanes  or 
buckets  may  be  analyzed.     The  motion  of  the  vane  has  been 


22 


STEAM-TURBINES. 


Figs.  10  and  11. 


ACTIOX  OF  STEAM   UPOX   TURBINE-BUCKETS.  23 

assumetl  to  b(>  in  a  straight  line,  and  this  assumption  will  be 
made  in  constructing  velocity  diagrams.  The  methods  to  be 
used  are  simpler  than  the  preceding,  but  the  work  that  has  been 
given  is  useful  in  showing  the  general  character  of  the  action 
between  the  buckets  and  the  working  fluid. 

Efficiency  of  the  Impulse-turbine. — Let  steam  enter  and 
leave  a  turbine-bucket  (Fig.  12;  with  relative  velocities  v  and  Vi 
respectively,  and  let  v=Vi.  Let  /9  =  J.  The  jet  enters  the 
turbine-casing  at  an  angle  a  with  the  direction  of  motion  of 
the  buckets,  and  the  entering  absolute  velocity  is  T^.  The 
absolute  exit  velocity  is  then  T^,  since  the  bucket  moves  with 
peripheral  velocity  u. 

The  energy  of  the  entering  jet  is  :^,  and  that  of  the  depart- 
ing  jet  is  -^.     The  work  done  upon  the  bucket  is  therefore 

The  velocity  diagram  as  shown  in  Fig.  13  may  be  repro- 
duced in  different  form,  as  shown  in  Fig.  11.  Revolving  Vi 
about  the  vertical  line  AD  until  Vi  coincides  with  v,  the  line 
representing  T^  will  take  the  position  AC  at  the  left  of  the  ver- 
tical. 

Solving  the  triangle  ABC  for  Vi^  in  terms  of  V  and  u, 

Vi^  =  V^^{2u)^-4Vu  cosa. 

The  efficiency  of  action  of  the  jet  upon  the  bucket  is  equal 
to  the  energy  given  up  by  the  jet  di\ided  by  the  total  energy 
of  the  entering  jet;  thus, 

y2-Y^2    72    y2_Y^2 
Efficiency  =  -^^  ^~  =  — p^— 

_  F2 -  [72  +  (2u)^-4:Vu  cos  a] 

Y2 


4u  I  u\ 

=  :^(^cosa-^j. 


^  Per  pound  of  steam. 


24 


STEAM-TURBINES. 


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ACTION  OF  STEAM  UPON   TURBINE-BUCKETS.  25 


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26  STEAM-TURBINES. 

It  is  evident  that  the  efficiency  depends  upon  the  relation 
between  peripheral  velocity  u,  entering  steam  velocity  F, 
and  the  angle  a  at  which  the  steam  leaves  the  nozzles.  If, 
as  is  generally  the  case  in  the  many-stage  turbine,  the  angles 
of  entrance  and  exit  are  not  equal,  the  above  expression  for 
efficiency  requires  modification. 

The  curves  on  the  preceding  page  show  the  variation  of 
efficiency  for  various  velocities  and  angles  of  entrance  of  the 
steam,  and  the  gain  accompanying  increase  of  peripheral 
velocity. 

MEANING  OF  THE   TERMS   'IMPULSE"    AND      REACTION" 
AS  USED   IN   THE   FOLLOWING   CHAPTERS. 

Since  the  forces  acting  in  the  two  types  of  turbine  are  due  to  two 

separate  although  closely  related  phenomena,  it  is  necessary  to  give 

distinctive  names  to  the  latter  in  order  to  state  methods  of  analsyis. 

Reference  should  be  made  to  pages  vii  to  x  in  the  Introduction,  and 

to  page  LSI  for  description,  and  method  employed  in  solving  the  problem. 

The  total  dynamic  pressure  exerted  by  a  stream  or  jet  passing  over 
a  blade  or  bucket  surface  and  experiencing  a  change  in  direction  of 
flow,  due  to  the  form  of  the  surface,  is  called  impulse.  Thus  the  action 
of  fluid  upon  vanes,  as  analyzed  on  pages  10  to  20,  results  in  impulsive 
pressure  entirely.  Reaction,  as  used  on  page  13,  is  to  be  understood 
as  meaning  that  part  of  the  total  impulsive  pressure  upon  the  surface 
which  is  caused  by  the  change  into  directions  of  flow  having  compo- 
nents opposite  to  the  direction  of  P,  Fig.  7.  P  represents  the  direc- 
tion in  which  it  is  desired  to  compute  the  impulsive  pressure  on  the 
vane.  The  word  Reaction  need  not  be  used,  however,  and  is  not  re- 
quired in  the  analysis  on  pages  11  and  12. 

Reaction  is  to  be  understood  as  the  pressure  opposite  in  direction 
to  that  of  flow,  resulting  from  and  accompanying  change  in  the 
velocity  of  the  steam.  If  the  steam  falls  in  pressure  during  its  passage 
through  a  row  of  blades  or  buckets,  its  motion  is  accelerated.  This  is 
accompanied  by  an  unbalanced  pressure,  or  reaction,  in  the  direction 
opposite  to  that  of  flow,  as  described  on  pages  67-70.  In  the  Parsoug 
turbine  impulse  and  reaction  combine  to  urge  onward  each  moving  blade 
and  in  order  to  analyze  the  acting  forces  it  is  necessary  to  discriminate 
between  the  two  methods  of  producing  pressure  against  the  moving 
elements  of  the  turbine. 


CHAPTER  11. 

THERMODYNAMIC   PRINCIPLES    IX\'OU^ED   IN   THE    FLOW    OP 

STEMI. 

"When  a  turbine  is  operated  by  steam  as  a  working  sub- 
stance, the  steam  is  so  conducted  through  the  machine  that 
it  gives  up  its  heat  energy  in  imparting  velocity  to  its  own 
particles.  The  result  is  a  stream  of  steam  more  or  less  nearly 
dry,  according  to  the  extent  to  which  heat  has  been  changed 
into  mechanical  work ;  and  this  mass,  travelling  at  high  velocity, 
strikes  against  the  rotating  parts  of  the  turbine  so  as  to  cause 
the  desired  motion. 

The  preceding  chapter  deals  with  the  principles  of  action 
of  a  stream  or  jet  as  it  strikes  against  and  leaves  the  turbine 
buckets.  The  present  chapter  deals  with  the  methods  used 
for  producing  the  jet  or  stream  of  Avorking  substance. 

The  problem  before  the  engineer  is,  to  produce  from  a  given 
amount  of  heat  energy  tlie  greatest  possible  kinetic  energy  in 
a  jet  of  steam  issuing  in  a  given  direction.  Tliis  means  that 
a  certain  weight  of  steam  must  attain  the  highest  possible 
velocity,  and  that  the  jet  must  be  conducted  in  the  most  effi- 
cient manner  to  the  point  at  which  it  is  to  dehver  its  energy 
to  the  buckets  or  blades  of  the  turbnie. 

While  the  design  of  nozzles  and  steam-passages  is  only 
one  among  a  great  many  problems  before  turbine  designers, 
it  is  of  great  importance  because  the  efficiency  of  the  nozzle 
determines  the  degree  of  economy  with  which  the  heat  energy 
of   the   steam   is   changed   into   mechanical   energy.     Recent 

27 


28  STEAM-TURBINES. 

investigations  show  that  the  fundamental  thermodynamic 
equations  for  the  flow  of  gases  must  he  used  with  great  cau- 
tion in  attempting  to  predict  results  of  the  flow  of  steam,  and 
that  the  special  conditions  under  which  the  steam  acts  in 
any  given  case  may  be  very  different  from  the  ideal  condi- 
tions assumed  as  the  basis  for  the  thermodynamic  equations. 
Further,  the  equation  developed  l^y  Zeuner,  which  has  been 
commonly  accepted  as  api)lying  to  steam  flow,  rests  upon 
the  assumption  of  a  constant  specific  heat  of  the  substance 
during  its  expansion,  and  therefore  does  not  apply  in  any 
but  a  roughly  approximate  manner  to  the  flow  of  a  varying 
mixture  of  steam  and  water.  Coefhcients  have  been  worked 
out  by  which  Zeuner's  equation  may  be  modified  so  as  to 
make  it  express  approximately  the  results  of  experiments  with 
different  forms  of  steam  orifices  and  nozzles,  but  the  results 
have  not,  so  far,  led  to  methods  of  predicting  what  may  be 
expected  to  occur  in  a  given  proposed  case. 

Steam  is  an  elastic  fluid,  and  it  has  the  power  of  expand- 
ing indefinitely  as  the  pressure  in  the  containing  space  is  fur- 
ther and  further  diminished.  This  power  of  expansion  is 
possessed  by  virtue  of  the  intrinsic  energy  of  the  steam,  or 
the  energy  due  to  the  heat  contents  of  the  steam.  Work 
has  been  done  upon  the  steam  in  supplying  it  with  heat  energy, 
and  the  steam  is  capable  of  increasing  its  volume  and  giving 
up  energy  to  other  bodies  of  matter  as  it  moves  them  out  of 
the  way,  and  thus  it  does  what  is  called  external  work.  Also, 
the  steam  in  expanding  experiences  changes  in  its  own  molec- 
ular activity;  its  temperature  and  pressure  are  lowered  as 
it  gives  up  its  heat  during  expansion,  and  these  changes  in 
the  internal  condition  of  the  steam  result  in  what  is  called 
internal  work.  The  work  done  in  displacing  the  surroundings 
as  the  steam  increases  its  volume  is  called  external  work. 

A  coiled  spring  presents  similar  conditions.  "When  it  has 
been  compressed  or  extended  by  work  done  upon  it,  the 
spring  is  capable  of  changing  its  length  and  of  exerting  force 
upon  other  bodies  while  doing  so.     The  change  in  the  condi- 


THE  FLOW  OF  STEAM.  29 

tion  of  the  parts  of  the  spring  itself  is  cahed  internal  work, 
and  the  energy  it  gives  up  to  other  bodies  is  called  external 
work.  During  a  boiler  explosion  steam  does  external  work  in 
rupturing  and  displacing  the  boiler  parts  and  in  displacing 
and  vibrating  the  atmosphere.  The  steam,  finding  it  {)ossible 
to  fall  in  pressure  and  temperature,  expei'icnces  a  change  in 
its  internal  condition,  and  this  change  results  from  what  is 
called  internal  work.  In  this  case  the  internal  work  is  nega- 
tive, since  it  is  accompanied  by  a  decrease  of  the  internal 
energy  of  the  steam. 

Imagine  a  gas-tight  vessel,  containing  air  or  gas  at  a  cer- 
tain pressure.  Let  heat  be  lost  by  radiation  from  the  walls. 
The  temperature  and  pressure  of  the  gas  will  fall,  and,  in  gen- 
eral, internal  work  will  be  done  in  changing  the  internal  energy 
of  the  gas.  The  volume  remains  constant,  and  therefore  no 
external  work  is  done. 

If  the  walls,  on  the  other  hand,  do  not  transmit  heat,  and  if, 
instead  of  the  gas  being  kept  at  constant  volume,  an  opening 
is  made  in  the  vessel,  a  flow  of  gas  will  occur  through  the  open- 
ing and  external  work  will  be  done  upon  the  outside  medium, 
supposing  the  pressure  in  the  latter  to  be  lower  than  that  of 
the  gas  in  the  vessel.  If,  however,  the  pressure  in  the  vessel  be 
lower  than  that  outside,  the  outside  medium  will  rush  in  and 
do  work  upon  the  gas,  raising  its  temperature  and 
pressure. 

In  the  first  case,  the  gas  rushes  out  of  the  vessel,  displacing 
some  of  the  external  atmosphere,  thus  doing  external  work, — 
and  it  also  changes  its  own  temperature  and  pressure,  thus  doing 
internal  work.  In  the  second  case,  the  external  atmosphere 
possesses  the  greater  energy  and  it  does  external  work  upon  the 
gas  in  the  vessel,  by  compressing  it  into  smaller  volume;  and  it 
does  internal  work  upon  it  by  increasing  its  temperature  and 
pressure.  In  both  cases  heat  is  expended,  and  both  external 
and  internal  work  are  done.  Only  in  the  case  of  the  gas-tight 
vessel  is  the  work  all  internal  work. 

Both  internal  and  external  work  are  done  at  the  expense 


30  STEAM-TURBINES. 

of  the  intrinsic  energy  of  any  fiuid,  whether  gas  or  air  or  steam, 
and  in  general  tlie  following  equation  may  be  written : 

Heat  expended  =  Internal  work  +  External  work. 

A  given  weight  of  gas  at  given  pressure  and  temperature 
occupies  a  certain  known  volume,  and  contains  a  known  amount 
of  heat  energy.  If  the  gas  be  caused  to  expand  at  constant 
temperature,  the  product  of  pressure  and  volume  remains  con- 
stant, or  its  condition  may  be  found  at  any  point  of  its  ex- 
pansion from  the  ecjuation 

pv  =  PiVi==p2V2,  etc. 

In  order  to  obtain  such  expansion,  however,  heat  must  be 
added  to  the  gas  continuously,  during  its  expansion,  in  just  suffi- 
cient quantities  to  restore  to  the  gas  the  heat  equivalent  of  the 
work  done.  The  gas  gives  up,  continuously,  its  internal  energy, 
to  overcome  whatever  external  resistance  may  be  opposed  to  its 
expansion.  Since  the  gas  receives  compensation  for  all  energy 
expended,  it  possesses  the  same  internal  energy  at  the  end  of 
expansion  that  it  did  before  it  commenced  to  expand.  Such  a 
process  is  known  as  isothermal  expansion,  and  the  equation 
of  the  isothermal  expansion  line  may  be  found  by  making  tem- 
perature constant  in  the  fundamental  equation  for  gases, 

pv^T^ 

m  T     '  ^     ' 

T  being  the  absolute  temperature  at  which  expansion  occurs. 
If  expansion  takes  place  from  pxVi   to  P2V2,  Fig.   15,  the 
external  work  is  represented  by  the  shaded  area  beneath  the 
curve  pv  =  piVi,  and  equals 


THE  FLOW  OF  STEAM. 


31 


It  is  shown  in  thermodynamics  that  if  a  gas  expands  adia- 
batically, — that  is,  without  receiving  or  giving  out  heat,  as 
heat, — the  equation  to  the  expansion  curve  may  be  written 

pi'"  =  piri"  =  p2^'2",  etc., 

where  n  is  the  ratio  of  the  specific  heats  of  the  gas  at  constant 
pressure  and  at  constant  volume  respectively. 


Fig.  15. 


Let  a  quantity  of  gas  be  at  the  state  piVi  (Fig.  16)  and  let 
it  expand  to  ^2^2  adiabatically.     The  external  work  is 


W=  /     pdv  =  p,vr  /     — 


n  — 1  [        \?"2 


n-l 


As  no  heat  is  supplied  to  the  gas  during  expansion,  the 
external  work  possible  is  limited  in  amount  according  to  the 


32 


STEAM-TURBINES. 


intrinsic  energy  of  the  gas  at  pi?'i.  The  capacity  of  the  gas  to  do 
work  is  measured  by  the  area  beneath  the  curve,  extended 
indefinitely  to  the  right,  and  the  axis  of  volume.  ^Vhen 
the  volume  becomes  indefinitely  great  the  gas  has  done  all  the 
external  work  it  is  capable  of  doing.    Since  V2  has  become 


Fig.  16. 


indefinitely  great,  —  —  0,  and  the  expression  for  the  work  done 

becomes  simply 


Tf  = 


PlVl 

n  —  1' 


This  measures  the  total  intrinsic  energy  of  the  gas,  or 
working  substance. 

The  intrinsic  energy  of  the  gas  at  a  is 


El 


PlVl 

''n-r 


and  at  h  it  is 


E2  = 


P2V2 

n  —  1 


THE  FLOW  OF  STEAM.  33 

When  a  body  receives  heat,  and  does  not  change  its  state 
ikiring  that  reception  of  heat,  its  temperature  rises,  and  the 
body  either  expands  in  volume,  or  its  pressure  increases.  Thus, 
according  to  the  assumption  that  rise  of  temperature  means 
increased  vibratory  activity  of  the  particles  composing  the 
body,  the  internal  kinetic  energy  is  increased.  The  internal 
condition  of  the  body  is  also  changed  to  the  extent  of  increasing 
the  distances  between  the  particles  of  the  body,  as  the  latter 
expands. 

Besides  the  changes  of  internal  energy,  the  expansion  of  the 
body  causes  displacement  of  any  substance  surrounding  it, 
or  opposing  its  expansion.  This  is  called  external  work.  Due 
to  the  increase  in  the  internal  or  intrinsic  energy  of  the  body 
by  the  addition  of  heat,  external  work  is  done  upon  the  sur- 
roundings of  the  body  by  the  action  of  the  heat  in  causing 
enlargement  of  the  space  occupied. 

Further,  if  the  substance  be  a  fluid  such  as  gas  or  steam, 
held  within  a  vessel  and  containing  a  given  amount  of  heat 
energy,  the  substance  will  flow  from  a  properh'  arranged  orifice 
in  the  containing  vessel,  if  the  orifice  opens  into  a  medium  of 
lower  pressure  than  that  in  the  vessel.  Thus  the  energy  of  the 
substance  will  be  utihzed  in  a  third  manner,  that  of  giving 
velocity  to  the  particles  composing  the  substance  and  thus 
increasing  its  kinetic  energy. 

Let  the  vessel  a  be  fitted  with  an  orifice  at  b,  with  weW- 
rounded  entrance  so  that  no  losses  occur  due  to  irregularity 
of  flow  at  entrance  to  the  orifice.  Further,  let  the  orifice  pre- 
sent no  frictional  resistances  to  the  flow  of  the  substance,  now 
supposed  to  be  a  gas.  Let  the  intrinsic  energy  of  the  gas  be 
called  El  and  E2,  w^hen  inside  the  vessel  and  the  nozzle  respect- 
ively. External  work  piVi  is  done  upon  each  pound  of  gas 
leaving  the  vessel,  and  each  pound  does  external  work  P2V2 
as  it  expands  in  the  nozzle.  The  kinetic  energy  due  to  the 
velocities    in     the     vessel    and    the    nozzle    respectively    are 

~n—  and   -^ —  per  pound  of  gas. 

Now,  if  the  flow  of  the  substance  is  adiabatic,  the  total 


34 


STEA  M-TURBINES. 


energy  in  the  gas  remains  the  same  at  all  times  during  the 
flow,  and  may  be  expressed  by  the  following  fundamental 
equation  for  the  flow  of  elastic  fluids: 

Vi  and  V2  representing  volumes  per  pound  of  the  substance 
at  pressures  pi  and  p2  respectively;   while  Vi  and  V2  repre- 


FiG.  17. 


sent  velocities.  The  velocity  T^i  in  the  vessel  is  usually  negli- 
gibly  small  compared  with  V2,  and  suppressing  —J-,  the  equa- 
tion  becomes 


72 

—  =  El  -  E2  +  PlVi  -  7)2^2. 


(8) 


Since  the  right-hand  member  of  the  equation  represents 
the  sum  of  the  chang?  in  internal  energy  and  the  external 
work  done  upon  and  by  the  substance  during  its  ex- 
])ansion  from  piri  to  P2V2,  and  since  the  changes  have  been 
due  solely  to  the  work  done  by  the  heat  energy  in  the  steam. 

Y2 

it  follows  that  the  resulting  kinetic  energy,  ^,  per  pound  of 
the  issuing  stream,  is  numerically  equal  to  the  amount  of  heat 


THE  FLOW  OF  STEAM.  35 

each  pound  of  the  substance  has  given  up  during  its  expansion 
from  piVi  to  7)2^2. 

■  If  the  total  heat  of  the  substance  at  piVi  be  called  Hi, 
and  that  at  P2V2  be  called  Ho,  then  for  each  pound  of  the  sub- 
stance the  energy  of  the  jet  flowing  fi'oni  the  nozzle  is 

72 

—  =(//i-i/2)X  778.  foot-pounds.      ...     (9) 

From  this  equation  may  be  calculated  the  velocity  that 
would  result  in  an  ideal  case  from  a  given  fall  in  heat  contents 
of  a  known  quantity  of  gas  or  steam,  if  the  flow  were  confined 
to  a  given  direction. 

Example. — Steam  flows  through  a  nozzle,  and  in  doing  so 
falls  in  pressure  to  such  an  extent  as  to  make  a  difference  of 
22.1  thermal  units  per  pound  between  the  initial  and  final 
heat  contents.  Calculate  the  resulting  velocity,  assuming  that 
there  are  no  losses  of  energy  in  the  nozzle. 

One  thermal  unit  =  778.  foot-pounds  of  energy. 

//i- 7/2  =  225.  B.T.U. 


V^VllS.  X225.  X64.4  =  3360.  ft.  per  second. 

The  following  development  of  Zeuner's  equation  is  given 
because,  while  it  does  not  apply  exactly  to  the  flow  of  steam, 
it  is  of  considerable  interest  in  all  thermodynamic  work,  and 
it  does  apply  directly  to  the  flow  of  a  fluid  the  value  of  whose 
ratio  of  specific  heats,  at  constant  pressure  and  constant  volume 
respectively,  does  not  change  during  the  flow.  It  is  of  par- 
ticular interest  since  it  indicates  that,  after  a  certain  diminu- 
tion of  the  lower  pressure  in  the  case  of  the  flow  of  a  substance 
from  a  higher  pressure  to  varying  lower  pressures,  the  rate  at 
which  the  substance  flows  does  not  increase.  The  rate  in- 
creases until  the  ratio  of  final  to  initial  pressure  reaches  a  cer- 
tain value,  after  which  no  further  increase  accompanies  a  fur- 
ther lowering  of  the  final  pressure.     The  equation  is  that  of  a 


36  STEAM-TURBINES. 

curve  which  reaches  a  maximum,  after  which  it  decreases  to 
zero.     (See  curves  No.  5,  on  pages  96,  97,  98). 
Equation  8  may  be  written 

F2     p,7ij      P2V2   ,  n 

77-= T ^  +PlVi-p2V2= 7(piVi-p2V2), 

2g     n  —  1     n  —  1     '  '  n  —  1^         /  ^  ^/> 

in  which  n  represents  the  ratio  of  the  specific  heats  of  the 
substance  at  constant  pressure  and  constant  volume  respect- 
ively. 

Remembering  that  piVi'^  =  p2V2'', 

n-l 


from  which 


vA"-^  P2 

P2V2=Piv,y-J      =pm[- 


s--fe)j-{f-r"^ 


If  the  area  of  the  orifice  is  a,  the  volume  emitted  per  second 
=  aV  and  if  ro  is  the  specific  volume  at  pressure  7)2,  the  weight 
discharged  per  second  is 

V2 

But  V2  =  vpY 

Therefore 


Weightpe.second  =  Tr^,J{?|2.)„4,l(2^)"-a""l.'10) 


THE  FLOW  OF  STEAM.  37 

Let  -^=r.     Then  the  weielit  W  becomes  a  maximum  when 

2  1+n 

h)n—{r)  «     becomes  a  maximum. 

Differentiating  with  respect  to  r,  and  equating  to  zero. 


2      1-1      /       1  \  i. 
—  (r)'*      -(l+— )r"=0. 

\_ 
Dividing  by  (r)", 

The  vakie  of   the   ratio  r(  =-- )   for  maximum  flow  of  air 

V     7)1/ 

under  adiabatic  conditions  is  0.528,  the  value  of  n  being  1.41. 
For  dry  saturated  steam  the  ratio  of  specific  heats  is  ordi- 
narily taken  as  1.135  which  gives  a  maximum  flow,  by  weight, 

when  ^^  =  0.577. 

The  above  equation  (No.  10)  is  plotted  on  Plates  IV,  V, 
and  VI,  and  the  curve  indicates  that  if  the  pressure  in  the 
receiving  vessel  should  be  reduced  to  zero,  the  weight  of  fluid 
discharged  by  the  orifice  or  nozzle  per  unit  of  time  would  be 
zero.  It  was  stated  on  page  35  that  the  reasoning  upon  which 
the  equation  was  developed  applied  to  substances  within  the 
limits  of  pressure  and  temperature  pertaining  to  a  given  physical 
state,  in  which  the  ratio  of  specific  heats,  n,  remains  constant. 
The  reasoning  is  correct,  and  experimenters  have  met  with 
some,  though  not  complete,  success  in  attempting  to  verify 
the  conclusions  regarding  adiabatic  expansion  of  gases.*  It 
has    been    demonstrated    experimentally    that    air,    and    that 

*  See  paper  by  "\Vni.  Froude,  "Engineering,"  London,  1872;  also  paper  by 
Professor  Flieguer,  Zeitschrift  des  Vereines  d.  Ingenieure,  1896. 


38  STEAM-TURBINES. 

gases  in  general,  in  flowing  from  higher  to  lower  pressures 
through  orifices,  increase  their  weight  of  flow  per  unit  of  time 
as  the  back  pressure  p2  is  reduced,  but  that  after  reduction 
of  7)2  to  about  0.52  pi  no  further  increase  in  rate  of  flow  can 
be  brought  about  by  further  reduction,  of  p2* 

The  experiments  of  Professor  Gutermuth,  plotted  upon 
Plates  IV,  V,  and  VI,  show  that  the  weight  of  steam  discharged 
per  second  does  reach  a  maximum,  as  the  equation  indicates 
that  a  perfect  gas  should  do,  but  that  the  flow  of  steam,  instead 
of  decreasing  in  rate  after  the  maximum  has  been  reached, 
remains  constant  no  matter  how  much  the  back  pressure  be 
further  reduced. 

//  the  lower  'pressure,  p-j,  he  kept  constant,  and  the  initial 
pressure  be  increased,  the  rate  of  flow,  by  weight,  will  increase 
in  direct  proportion  to  the  increase  in  initial  pressure.  Experi- 
mental e\adence  as  to  this  and  as  to  the  statements  made  in 
the  preceding  discussion  will  be  given  during  the  development 
of  the  subject  of  the  flow  of  steam. 

*  See  bottom  of  page  62. 


CHAPTER    III. 

GRAPHICAL   REPRESEXTATIOX   OF   WORK   DONE  IN   HEAT 
TRANSFORMATIONS. 

The  pressure-volume  diagram,  of  which  the  ordinary  steam- 
engine  indicator  card  is  an  example,  and  the  heat  diagram, 
or,  as  it  is  generally  called,  the  temperature-entropy  diagram, 
are  two  means  by  which  the  effect  of  transforming  heat  into 
mechanical  work  is  represented.  The  present  chapter  wiU. 
discuss  the  heat  diagram,  which  serves  a  purpose  distinct  from 
that  of  the  work,  or  pressure-volume  diagram.  Either  method 
of  repi-asentation  taken  alone  is  incomplete  without  the  other, 
wliile  the  two  together  completely  satisfy  the  requii'ements 
in  analyzing  graphically  a  thermodynamic  problem  from  an 
engineering  standpoint. 

In  Fig.  18  let  ordinates  represent  absolute  temperature. 
It  is  required  to  construct  a  diagram  whose  area  shall  represent 
heat  quantities  in  thermal  units,  and  absolute  temperature 
is  required  to  be  used  as  one  dimension  of  the  heat  represented 
by  the  diagram.  This  is  done  because  temperature  is  the 
intensity  factor  of  a  heat  quantity,  and  absolute  temperature 
is  used  because  the  fundamental  laws  of  thermodjmamics  are, 
as  they  are  now  understood,  based  upon  the  scale  of  absolute 
temperature.  The  adoption  of  this  scale  in  the  heat  diagram 
thus  relates  computations  made  from  the  diagram  to  those 
made  by  the  laws  of  heat  as  ordinarily  expressed.  It  is  required 
to  find  another  function  which  taken  as  an  abscissa  in  con- 
nection with  absolute  temperature  as  an  ordinate  will  give 

39 


40 


STEAM-TURBINES. 


a  diagram  whose  area  represents  heat-units,  as  described  above. 
It  is  well  in  approaching  the  heat  diagram  for  the  first  time  to 
start  without  any  thought  of  entropy,  unless  one  has  a  very 


T3 

B 

/ 

Ti 

/ 

\ 

B 

T, 

A 

^ 

b 

^ 

m 

^ 

5g 

k 

^ 

> 

r^ 

AREA 

tiQ 

-^ 

>/y 

^ 

^ 

?% 

%. 

%. 

D 

%^- 

■^ 

C 

T?, 

"D 

C 

- 

0 

El 

E2 

0 

El 

1  - 

E2 

F 

g.l 

8. 

F 

ig. 

20. 

P 

a 

k 

v> 

k^ 

\ 

:^^ 

X 

T, 

^ 

e;^; 

r'/^ 

V)> 

\ 

^ 

^ 

^ 

^ 

lg 

^ 

^ 

t 

J« 

^ 

^ 

^ 

c 

, 

( 

3 

I 

?«, 

p 

1  n 

;l- 

V 

clear  notion  of  the  meaning  of  that  word,  and  to  simply  deter- 
mine for  one's  self  the  character  of  the  abscissa  of  the  heat 
diagram.  This  will  later  be  found  to  be  the  same  as  the  func- 
tion to  which  the  name  entropy  was  given  by  early  investi- 
gators of  the  science  of  heat. 


WORK  DONE  IN  HEAT  TRANSFORMATIONS.  41 

Let  the  quantity  which  i>s  to  bo  i-epichX'iitecl  by  abscissa 
always  increase  when  heat,  as  heat,  is  added  to  a  substance, 
and  decrease  when  heat,  as  heat,  is  taken  away.  A  vertical 
line  then  represents  a  set  of  conditions  in  which  the  tempera- 
ture changes,  l^ut  during  the  change  there  is  no  heat,  as  heat, 
given  to  or  taken  away  from  the  substance.  This  is  what 
is  called  an  adiabatic  process,  which  means  that  no  heat,  as 
heat,  has  been  given  to  or  taken  away  from  the  working  sub- 
stance during  the  process.  In  other  words,  the  vertical  line 
is  what  is  called  an  adiabatic. 

A\Tiile  the  word  "  adiabatic  "  means  that  no  heat  com- 
munication takes  place  between  the  working  substance  and 
other  bodies  during  the  process  in  question,  there  is  always 
work  done  when  a  substance  expands  against  a  resistance, 
and  this  work  is  done  at  the  expense  of  the  heat  cnergj-  pos- 
sessed b}''  the  boch\  Therefore  during  adiabatic  expansion 
heat  does  leave  the  substance  as  work  done,  but  not  in  the 
form  of  heat.  The  adiabatic  curve  in  the  pressure-volume 
diagram,  and  the  vertical  or  adiabatic  line  in  the  heat  diagram, 
represent  a  change  during  which  work  is  done,  and  therefore 
the  intrinsic  energy  of  the  working  substance  is  diminished; 
but  during  the  process  no  heat  has  been  given  to  or  taken 
from  the  working  substance,  excepting  as  heat  has  been  trans- 
formed into  mechanical  energy.  A  horizontal  line  I'epresents 
a  process  during  which  heat  is  added  to  or  abstracted  from  a 
substance  at  a  constant  temperature;  that  is,  there  is  no 
temperature  change  during  the  process.  A  horizontal  line 
then  represents  in  the  diagram  what  is  called  an  isothermal 
change,  or  a  change  at  constant  temperature,  and  the  function 
which  is  to  be  found  and  used  as  abscissae  in  the  diagram  is 
the  scale  by  which  the  relation  between  different  adiabatic 
changes  is  expressed.  Thus  in  Fig.  18,  AD  represents  an  adia- 
batic change  in  which  a  substance  whose  temperature  was 
originally  that  represented  at  the  height  A  has  fallen  in  tem- 
perature to  D  without  having  received  or  given  up  any  heat 
as  heat.    The  line  BC  represents  a  similar  adiabatic  drop  in 


42  STEAM-TURBINES. 

temperature.  The  horizontal  hne  AB  is  a  line  of  constant 
temperature,  and  the  distance  AB  or  E1E2  represents  the 
change  of  abscissa  corresponding  to  a  change  in  heat  con- 
tents measured  b}^  the  area  ABEoEi.  AB  is  what  is  called 
an  isothermal  line,  and  a  quantity  of  heat  represented  by  the 
area  ABE2E1,  under  the  line  AB  and  extending  to  the  line 
of  zero  absolute  temperature,  has  been  added  to  the  substance, 
thereby  moving  the  point  representing  the  state  or  condition 
of  the  substance,  from  A  to  B.  The  state  of  the  substance, 
represented  by  the  point  A,  shows  that  its  temperature  is  Ti. 
The  method  by  which  this  temperature  was  attained  is  not 
shown,  and  it  is  not  necessary  that  it  be  known  in  order  that 
the  effect  of  further  operations  may  be  represented.  If  heat 
is  added  to  the  substance  isothermally,  the  state  point  will 
move  from  A  to  B,  and  the  tlistance  AB  will  be  such  that 
the  heat  that  has  been  added  equals  the  area  ABEjEy. 

To  make  the  above  clear,  suppose  in  Fig.  19  the  ordinates 
and  abscissa?  represent  pressure  and  volume  respectively. 
Then  the  familiar  Carnot  cycle  will  be  represented  by  two 
isothermals  ah  and  cd  intercepted  by  two  adiabatics  he  and  da. 
The  cycle  is  represented  in  Fig.  18  by  the  figure  ABCD.  The 
mechanical  equivalent  of  the  heat  involved  in  the  cycle  Fig. 
19  is  represented  by  the  area  abckl,  and  in  the  heat  diagram 
Fig.  18  the  heat  involved  in  the  process  is  represented-by  ABE2E1. 
The  mechanical  equivalent  of  the  heat  rejected  at  the  lower 
temperature  To  is  represented  in  Fig.  19  by  the  area  cdmk, 
and  in  Fig.  18  the  heat  is  represented  by  the  area  CDE1E2. 
The  shaded  area  in  each  of  the  figures  represents  the  net  work 
accomplished  during  the  cycle.  In  the  heat  diagram  the  area 
ABCD  represents  heat-units  utilized  during  the  cycle,  and  in 
the  pressure-volume  diagram,  Fig.  19,  the  area  abed  represents 
the  work  realized  in  foot-pounds.  The  efficiency  of  the  cycle 
represented  in  Fig.  19  is 

Ti-T2 


WORK  DONE  IN  HEAT   TRANSFORMATIONS.  43 

and  it  is  easy  to  see  that  the  cycle  represented  in  Fig.  18  has 
the  same  efficiency;  that  is,  the  shaded  area  ABCD  divided 
by  the  area  ABE2E1  is  the  efficiency  of  the  cycle,  and  this 
obviously  equals 

Ti     • 

If  the  total  heat  beneath  the  line  AB,  Fig.  18,  that  is,  the 
heat  ABE-yEi,  equals  Q,  then  the  heat  transformed  into  use- 
ful work  during  the  cycle  equals 

^X  (7^1 -7^2). 

The  quantity  7^   is  obviously  a  measure  of  the  distance 
-t  1 

EiEo,  or  it  is  what  is  commonly  called  the  increase  of  entropy 
occurring  between  the  initial  and  final  states  A  and  B  respec- 
tively.    For  an  isothermal  change,  then,  the  change  in  entropy 

is  equal  to  ^,  where  T  represents  the  absolute  temperature  at 

which  the  heat  Q  is  received. 

Absolute  quantities  of  entrop}^  are  not  measured,  but  only  the 
differences  of  entropy  between  two  states  of  a  substance,  as  the 
total  value  of  the  entropy  above  absolute  zero  is  not  known, 
and  is  not  necessary  for  engineering  purposes. 

Suppose  that  the  state  of  a  substance  is  represented  (Fig.  20) 
by  the  point  A,  and  heat  be  added  to  the  substance,  raising  its 
temperature.  The  substance  may  be  considered  to  be  any 
soUd  which  is  heated  without  experiencing  a  change  in  its 
state,  as  from  solid  to  liquid,  liquid  to  gaseous,  etc.,  or  it  may 
be  a  gas  supposed  to  not  change  its  state  during  the  heat  change 
under  consideration.  In  Fig.  18  heat  was  added  isothermally, 
as  when  a  sul^stance  like  water  is  evaporated,  along  the  line  AB; 
but  if  at  the  point  A  (Fig.  18)  the  substance  had  been  water 
below  its  boiling  temperature,  then  if  heat  had  been  added  to 


44  STEAM-TURBINES. 

it,  a  rise  in  temperature  would  have  occurred  along  some  such 
curve  as  AB  (Fig.  20).  Now,  let  the  heat  diagram  that  is 
to  be  constructed  be  such  that  the  area  underneath  any  line, 
as  the  line  AB,  down  to  absolute  zero  of  temperature,  repre- 
sent the  total  heat  involved  in  the  process;  then  the  heat  added 
to  move  the  state  point  from  A  to  B  is  that  represented  by 
the  area  ABE2E1,  Fig.  20.  If  one  pound  of  the  substance  is 
supposed  to  be  involved  in  the  process,  ha\'ing  a  specific  heat 
of  S,  then  the  heat  that  caused  the  rise  in  temperature  from  Ti 
to  Ts  is  represented  by  the  area  ABE2E1  and  is  equal  to 
S(Ts  —  Ti).  This  follows  from  the  definition  of  specific  heat. 
Let  the  quantity  of  heat  be  called  Q,  as  was  done  in  the  case  of 
the  isothermal  addition  of  heat  along  AB  in  the  discussion  of 
Fig.  18.  It  is  desired  to  do  for  the  diagram  in  Fig.  20  just 
what  was  done  for  that  in  Fig.  18,  that  is,  to  find  the  increase 
in  the  value  of  the  abscissa  due  to  the  addition  of  the  heat  Q. 
In  the  case  of  the  rectangular  diagram  of  Fig.  18  it  was  a  simple 
matter  to  divide  the  area  of  the  rectangle  by  one  dimension, 
or  the  increase  of  the  abscissa  E1E2.     This  was  found  to  be 

■^,  and  this  quantity  multiplied  by  the  temperature  range 
-/ 1 

(T1—T2)  gave  the  total  heat  utilized  during  the  cycle.  In  Fig. 
20  the  cycle  begins  with  an  addition  of  heat  to  a  body  having 
absolute  temperature  Ti.  The  result  is  a  rise  of  the  tempera- 
ture of  the  body  to  T^  and  a  change  of  position  on  the  diagram 
of  the  state  point  to  B.  The  quantity  of  heat  Q  causing  tliis 
rise  is  represented  by  the  area  between  AB  and  the  line  of  zero 
temperature,  that  is,  by  the  area  ABEiEi.  The  next  step  in 
the  cycle  is  an  adiabatic  expansion  of  the  body  from  Tz  to  T2, 
and  this  expansion  is  represented  by  the  vertical  line  BC.  Just 
as  in  the  Carnot  cycle  of  Fig.  18,  heat  is  rejected  or  exhausted 
along  the  isothermal  CD,  and  the  body  is  brought  to  its  original 
condition  at  .4.  by  an  adiabatic  compression  along  the  vertical  hue 
DA.  The  only  difference  between  the  two  cycles  is  that  heat 
was  added  isothermally  in  that  of  Fig.  IS,  and  with  a  rising 
temperature  in  Fig.  20. 


WORK  DONE  IN  HEAT   TRANSFORMATIONS.  45 

Returning  to  the  equation  last  written,  the  quantity  of 
heat  added  is 

Q  =  S{T^-T,). 

This,  however,  gives  no  clue  to  the  amount  by  which  the 
abscissa  of  the  diagram  has  been  increased,  and  it  is  this  quantity 
which  is  required  in  order  to  make  it  possible  to  trace  out  the 
path  by  which  the  state  point  moved  from  A  to  B  during 
the  addition  of  the  heat  Q. 

The  area  ABEoEi  may  be  divided  into  ver}'  small  areas, 
similar  to  the  area  clQ  in  Fig.  20,  and  if  the  width  of  each  of 
these  is  given  the  indefinitely  small  value  clE,  then  the  vertical 
height,  or  the  absolute  temperature  at  wliich  the  heat  repre- 
sented by  dQ  is  added,  may  be  considered  as  constant  during 
the  addition  of  the  heat  dQ.  An  equation  may  then  be  WTitten 
thus: 

dQ  =  TdE, 

where   T  represents   the   absolute   temperature  at  which  dQ 
is  added  to  the  substance. 
Similarly  the  equation 

may  be  made  to  express  the  heat  represented  by  the  area  dQ 
by  making  use  of  the  fact  that  during  the  addition  of  dQ  the 
rise  of  temperature  is  only  an  infinitesimal  amount  dT  instead 
of  {Tz  —  Ti).     The  expression  thus  becomes 

dQ  =  SdT. 

The  two  expressions  for  dQ  may  now  be  equated  thus: 

dQ  =  TdE=SdT 


GT 


dE  =  S~. 


.    46  STEAM-TURBINES. 

The  distance  E1E2  is  equal  to  the  sum  of  all  the  small  dis- 
tances like  dE,  and  therefore  the  distance  E1E2  or  the  total  in- 
crease of  the  abscissa  of  the  state  point  during  the  change  of  the 
temperature  of  the  substance  from  Ti  to  T3  is  equal  to  the 

dT 
summation  of  all   the  quantities  S-^r  between  the  limits  of 

temperature    Ti  and  T^.      Expressing    this   in   mathematical 
form 


Stating  briefly  the  substance  of  the  preceding  discussion: 

I.  The  ordinate  of  the  point  representing  the  state  of  the 
working  substance  as  to  temperature  and  heat  changes  in- 
creases and  decreases  as  the  absolute  temperature  of  the  sub- 
stance rises  and  falls. 

II.  The  abscissa  of  the  state  point  increases  and  decreases 
during  addition  and  abstraction  of  heat  respectively,  and  the 
amount  by  which  it  changes  is  expressed  in  the  two  following 
ways : 

(a)  The  increase  or  decrease  is 


F      ^ 
E  =  Y,' 


when  heat  is  added  or  abstracted  at  a  constant  temperature 
Ti,  as  in  the  boiUng  of  water  and  the  condensation  of  steam. 
(6)  The  increase  or  decrease  is 

^=.s:iog^,^^, 

when  heat  is  added  or  abstracted  and  thereby  raises  or  lowers 
the  temperature  of  the  substance  from  T^i  to  T's,  as  in  the  heat- 
ing or  cooling  of  a  gas  between  such  limits  of  temperature 
that  the  physical  state  of  the  gas  does  not  change  in  the  process. 


WORK  DONE  IX  HEAT   TRANSFORMATIONS.  47 

In  the  above,  S  is  the  mean  specific  heat  of  the  substance 
between  the  temperatures  Ti  and  T3. 

Let  a  pound  of  water  be  at  493  degrees  F.  absolute  tem- 
perature, corresponchng  to  about  32  degrees  on  the  ordinary 
Fahrenheit  scale.  The  water  is  then  at  the  temperature  at 
which  ice  melts.  As  a  matter  of  convenience  the  tables  giving 
the  properties  of  water  and  steam  have  been  commenced  at 
this  temperature.  Since  the  total  value  of  the  entropy  of  the 
substance  is  not  used  in  computation,  but  only  the  increases 
or  diminutions  of  entropy  due  to  additions  and  abstractions 
of  heat  respectively,  the  line  representing  zero  entropy  may 
be  located  in  any  convenient  position.  Steam-engine  prob- 
lems are  ordinarily  concerned  with  the  properties  of  water  and 
steam  above  the  melting-point,  and  therefore  the  line  of  zero 
entropy  may  be  conveniently  placed  so  as  to  disregard  the 
heat  that  exists  in  the  water  before  it  reaches  the  temperature 


Reason  for  the  use  of  the  term  Entropy. 

The  expressions  —  and  /  -^  have  been  used  since  the  researches  of  Clausius 

and  Rankine,  and  are  of  fundamental  importance  in  analyzing  heat  problems. 

The  name  Entropy  was  applied  by  Professor  Clausius  to  the  general  ex- 
pression j  — ,  and  Professor  Rankine  called  it  "  The  Thermodynamic  Func- 
tion." Rankine  used  the  Greek  letter  (f)  to  represent  the  function,  and 
various  writers  using  the  Greek  letter  0  to  represent  absolute  tempera- 
ture have  called  the  heat  diagram  "  The  Theta-phi-diagram."  The  name 
generally  given  to  it,  however,  is  "  The  Temperature-entropy  Diagram." 
A  discussion  of  reversible  and  irreversible  processes  is  involved  in  satis- 
factorily explaining  the  meaning  and  application  of  the  term  "Entropy," 
and  for  such  discussion  recourse  may  be  had  to  the  works  of  Clausius,  Zeuner, 
Rankine,  and  other  writers  upon  thermodynamics.  The  following  articles 
discuss  the  recent  literature  of  the  subject: 

"On  Clausius'  Theorem  for  Irre\ersible  Cycles,  and  the  Increase  of 
Entropy,"  by  W.  McF.  Orr,  Philosophical  Magazine,  Vol.  8,  1904,  page  509. 

"  On  Certain  Difficulties  which  are  Encountered  in  the  Study  of  Ther- 
modynamics," by  Dr.  Edward  Buckingham,  Phil.  Mag.  ^'ol.  9,   1905. 


48  STEAM-TURBINES. 

of  melting  ice  at  the  mean  barometric  pressure.  The  diagram 
on  Plate  I  must  be  imagined  to  extend  below  the  line  of 
490  degrees  absolute  down  to  absolute  zero.  The  total  area 
beneath  any  line  representing  a  continuous  change  in  the  con- 
dition of  the  substance,  and  down  to  absolute  zero  of  tem- 
perature, represents  the  British  Thermal  Units  involved  in  the 
change. 

The  curve  XAB  represents  the  addition  of  heat  to  water, 
thus  raising  its  temperature  from  that  of  melting  ice  to  higher 
temperatures.  The  increase  in  entropy  from  493  to  750  degrees 
is  approximately 

^5  =  *S  log,  ^  =  1X0.42. 

i  2 

The  entropy  of  the  point  B  is  seen  to  correspond  with  this 
value. 

The  specific  heat  of  water,  S,  is  not  constant,  and  on  a  rigid 
computation  for  change  of  entropy  over  a  range  of  temperature 
it  is  necessary  to  take  the  mean  specific  heat  for  the  tempera- 
ture range  in  question.  Within  the  limits  just  used  the  mean 
value  for  S  is  1.006,  or  very  nearly  unity.  In  steam-engine 
problems  in  general  the  value  of  unity  may  be  used  without 
any  greater  error  than  is  always  involved  in  reading  results 
during  engine  tests  The  total  heat  above  that  at  freezing- 
point  in  the  pound  of  water  at  B  is 

Hb  =  S{T,  -To)  =  l  .006(750  -  493)  =  258.0  B.T.U. 

By  looking  in  the  steam-tables  for  the  heat  of  the  liquid 
above  32  degrees  corresponding  to  750  degrees  this  value  will 
be  found. 

The  curve  AB  represents  the  heating  and  cooling  of  water, 
and  its  equation  is 

T 

Change  of  entropy  =  *S  log^  ^. 

i  2 


WORK  DONE  IN  HEAT  TRANSFORMATIONS. 


49 


PLATE  L 


oi    ei     A 


Absolute  Temperature  Fahrenheit 
ti^w     CT^j      «b»—     M^ 


«o     ts     o 


!-=      o     c:     c>    o 


50  STEAM-TURBINES. 

The  line  BC  is  an  isothermal,  or  line  of  constant  tempera- 
ture, and  represents  the  addition  of  the  heat  of  vaporization 
to  water  of  the  temperature  represented  by  the  height  of  the 
line.  Water  at  B  is  just  ready  to  become  steam,  and  a  slight 
addition  of  heat  generates  a  correspondingly  small  quantity  of 
steam. 

By  experiment  it  has  been  found  that  if  to  the  pound  of 
water  at  750  degrees  absolute  temperature  there  be  added 
about  911  heat-units  the  water  will  be  completely  evaporated 
into  dry  steam.  The  total  heat  above  32  degrees  would  then 
be 

258.6  +  911  =  1169.6. 

By  consulting  the  steam-tables  this  will  be  found  to  be  the 
value  given  for  the  total  heat  above  32  degrees  of  the  ordinary 
scale,  or  above  493  degrees  absolute. 

If  only  half  of  911  heat-units  had  been  added  to  the  water 
at  B  only  half  a  pound  of  steam  would  have  been  formed,  or 
the  "quality"  of  the  steam  would  have  been  50%.  It  will 
be  found  by  measurement  that  the  curve  on  the  diagram 
marked  50^  divides  each  horizontal  distance  such  as  BC  into 
two  equal  parts.  Similarly,  the  curve  marked  90%  divides 
the  distance  into  parts  which  are  to  each  other  as  9  is  to  1. 
This  means  that  if  the  addition  of  heat  at  a  given  tempera- 
ture should  be  stopped  at  the  intersection  of  this  curve  with 
the  horizontal  line  representing  the  given  temperature,  90% 
of  the  heat  necessary  to  evaporate  a  pound  of  water  into  dry 
steam  would  have  been  added,  or  there  would  be  produced 
0.9  pound  of  steam.  The  remaining  0.1  would  remain  as 
water,  either  in  the  boiler  or  suspended  in  the  steam. 

The  curve  CF  is  called  the  "Saturation  Curve,"  and  is 
drawn  through  the  extremities  of  the  horizontal  hnes  represent- 
ing the  increase  of  entropy  accompanying  the  addition  of 
sufficient  heat  at  dilTerent  temperatures  to  completely  vaporize 
a  pound  of  water  at  these  temperatures. 


WORK  DONE  IN  HEAT   TRANSFORMATIONS.  51 

The  area  beneath  the  line  BC,  down  to  absolute  zero  of 
temperature,  represents  the  heat  of  vaporization  or  the  "latent 
heat "  of  a  pound  of  steam  at  the  temperature  750  degrees 
absolute.  The  increase  of  entropy  between  B  and  C  is  found 
by  dividing  the  heat  of  vaporization  by  the  absolute  tempera- 
ture at  which  it  is  added,  or 


£«.  =  §  =  1.215. 


This  may  be   verified   by  subtracting  E^  from  Ec  on  the  dia- 
gram. 

The  curves  marked  1100  B.T.U.,  1000  B.T.U.,  etc.,  cut  the 
horizontal  lines  in  such  points  that  if  the  addition  of  heat  should 
be  stopped  at  these  intersections  the  pound  of  steam  and  water 
would  contain  the  amount  of  heat  indicated  by  the  figures  on 
the  curve.  Thus,  if  heat  were  added  along  BC  till  the  entropy 
increased  to  that  at  H,  the  pound  of  steam  and  water  would 
contain  1100  B.T.U.   above  the  temperature  of   melting  ice. 

RfJ 

The  fraction  -jj^  of  the  total  heat  of  vaporization  present  is, 

approximately, 

^,  =  J-^X911  =  842  + 

Heat  of  liquid  Hb=  258 -f- 


Total  heat  above  freezing  1100  B.T.U. 

If  heat  be  added  to  the  steam  after  it  has  become  dry  and 
saturated,  as  at  C,  the  result  is  the  production  of  what  is  called 
" swperheated  steam."  As  heat  is  added  to  it,  the  tempera- 
ture rises;  that  is,  the  "  degrees  of  superheat  "  increase.  Super- 
heated steam  behaves  much  as  does  a  gas.  The  curve  CD  has 
the  same  equation  as  the  curve  AB,  with  the  exception  that 
the  value  of  the  specific  heat  is  different,  and  the  increase  of 


52  STEAM-TURBINES. 

entropy  accompanying  an  increase  of  temperature  from  Tc 
to  Td  is 

^  =  ^log,^, 

where  S  is  the  mean  specific  heat  of  superheated  steam  for  the 
range  in  question. 

Taking  0.57  as  the  specific  heat,  the  increase  of  entropy 
during  addition  of  heat  from  C  to  D  is 

Eci>  =  0.57  log,  ;^  =  0.57X0.199  =0.113. 
'^  /  00 

This  will  be  found  to  correspond  approximately  with  the  value 
given  on  the  diagram. 

The  heat  involved  in  raising  the  temperature  of  steam 
from  the  saturation  temperature  at  C  of  750  degs.  to  920  degs. 
is 

/f,  =  0.57(920 -750)  =0.57X170  =  97  B.T.U.,  approximately. 

The  total  heat  in  the  superheated  steam,  then,  above 
32  degs.  F.  is 

258+911  +  97  =  1266  B.T.U. 

It  will  be  evident,  upon  finding  the  area  beneath  the  broken 
line  XBCD  down  to  absolute  zero,  or  490  degs.  below  the 
base  line  of  the  diagram,  that  this  area  represents  the  number 
of  thermal  units  stated.  The  dimensions  in  which  the  area 
is  measured  are  the  same  as  those  representing  degrees  tem- 
perature, and  entropy  units.  Thus,  the  heat  under  the  line  BC 
is  represented  by  an  area  1.215  units  in  width  horizontally 
and  750  units  vertically,  giving  911  thermal  units  as  the  heat 
so  represented. 

Curves  of  constant  pressure  such  as  CD  are  plotted   by 


WORK  DONE  IN  HEAT  TRANSFORMATIONS.  53 

the  methods  of  the  last  example,  which  give  the  increase  in 
entropy  accompanying  any  rise  in  temperature,  as  from 
C  to  D.  The  point  C  represents  the  state  of  a  pound  of  dry 
steam  at  normal  temperature  corresponding  to  its  pressure. 
The  steam  contains  in  that  condition  a  certain  amount  of 
heat  which  is  different  from  the  amount  contained  in  a  simi- 
lar amount  of  dry  steam  at  any  other  pressure.  The  line  CD 
represents  the  addition  of  heat  to  the  normal  amount  of  heat 
at  C.  The  value  of  S  to  be  used  in  the  equation  for  the  Une  CD 
is  the  specific  heat  *  of  superheated  steam  at  constant  pressure ; 
that  is,  it  is  the  numl^er  of  thermal  units  required  to  raise  a 
pound  of  steam  of  pressure  corresponding  to  a  certain  tem- 
perature, by  one  degree  Fahrenheit.  If  the  specific  heat  is 
constant  for  all  pressures  and  temperatures  then  one  value 
is  to  be  used  in  all  cases.  If  it  changes  when  the  pressure 
changes  then  a  different  value  must  be  used  for  each  pressure. 
If  it  changes  as  the  temperature  changes,  then  for  a  given  tem- 
perature range  a  mean  value  must  be  found  which,  when  mul- 
tiplied by  the  temperature  range,  will  give  the  quantity  of 
heat  required  to  cause  the  rise  of  temperature  involved. 

In  any  case,  since  the  superheat  indicated  by  the  area 
beneath  CD  is  the  heat  necessary  to  raise  dry  steam  of  the  tem- 
perature and  pressure  indicated  at  C,  and  does  not  apply  to 
the  superheat  for  any  other  pressure,  the  line  CD  is  properly 
called  a  ''  line  of  constant  pressure." 

Lines  of  constant  heat  such  as  those  marked  1200-1190^ 
etc.,   may  be   drawn  as  follows: 

The  total  heat  above  493°  abs.  in  dry  steam  at  C  has  been 
found  to  be  1169.6  B.T.U.  Let  it  be  required  to  plot  a  line 
of  which  each  point  shall  represent  superheated  steam  con- 
taining 1200  B.T.U.  per  pound.  One  point  of  the  line  may 
be  found  on  the  constant-pressure  line  CD.  The  heat  at  C 
being  1169.6  B.T.U.,  it  will  be  necessary  to  add  30.4  B.T.U. 
to  dry  steam  in  order  to  produce  superheated  steam  contain- 

*  The  value  of  the  specific  heat  used  in  plotting  the  curves  in  the  diagram 
on  the  back  cover  of  the  book  is  0.58. 


54  STEAM-TURBINES. 

ing  1200  B.T.U.  per  pound.  If  S  is  the  specific  heat  at  the 
pressure  represented  by  CD,  then  the  rise  of  temperature  corre- 
sponding to  the  addition  of  30.4  B.T.U.  per  pound  may  be 
found  from  the  equation 

SO  A=S(Tg-Tc). 

Calling  the  value  of  S  equal  to  0.57  as  before, 

30.4  =  0.57(7^G -750), 
or 

Tg  =803.3  degs. 

This  fixes  one  point  of  the  constant-heat  curve  for  1200 
B.T.U.  per  pound.  A  similar  method  may  be  followed  along 
all  constant-pressure  curves  for  finding  the  required  series  of 
constant-heat  curves. 

EXAMPLES   IX   THE    USE   OF  THE   HEAT   DIAGRAM. 

Let  a  pound  of  water  be  at  temperature  600°  abs.,  repre- 
sented by  the  point  A,  page  49.  It  contains  sufficient  heat 
above  the  melting-point  of  ice  to  have  raised  its  temperature 
from  that  point,  or  493°,  to  its  present  temperature  of  600°, 
and  during  that  rise  in  temperature  its  entropy  value  has 
been  increased  from  the  arbitrarily  assumed  zero  to  the  value 
0.20.  Let  heat  be  added  to  the  water  sufficient  to  raise  its 
temperature  to  750°  abs.  The  quantity  of  heat  necessary 
may  be  found  from  the  steam-tables  by  subtracting  the  heat 
of  the  liquid  at  600°  from  that  at  750°. 

Thus,  heat  of  liquid  at  7.50  =258.6  B.T.U. 

"     "      ''      "  600  =107.2  B.T.U. 


Heat  involved,  represented  by  the 
area  beneath  the  curve  AB,         =151.4  B.T.U. 


WORK  DONE  IN  HEAT   TRANSFORMATIONS  55 

Or  this  miglit  have  been  found  thus: 

Temperature  range  =  750°  -  600°  =  150°. 
Mean    specific    heat   of   water    between    the    temperatures 
=  1.008. 

Heat  of  hquid 

=  ///,  =,S(r5-r^)  =  1.008xl50  =  151.4B.T.U. 

(a)  If  the  pound  of  water  were  part  of  the  contents  of  a 
steam-boiler  carrying  57  pds.  pressure  per  sq.  inch  (correspond- 
ing to  750  deg.)  and  a  valve  were  suddenly  opened  admitting 
the  water  into  a  large  tank  in  which  there  was  a  pressure  of 
only  2.8  pds.  abs.  (corresponding  to  600  deg.)  the  heat  in  the 
water  would  instantly  cause  vaporization  of  the  water  at  the 
lower  pressure  and  the  formation  of  a  great  amount  of  steam. 
If  the  valve  were  opened  suddenly  enough,  the  liberation  of 
heat  energy  caused  by  the  reduction  in  pressure  would  occur 
without  transfer  of  heat  to  the  surroundings,  excepting  as 
the  latter  were  disturbed  by  the  external  work  accompanying 
the  formation  of  steam.  The  process  would  then  be  adiabatic 
and  represented  by  the  line  BEi.  The  heat  available  for  the 
formation  of  steam  at  the  lower  temperature  and  pressure 
would  be  measured  by  the  area  ABEiA  and  would  be  equal 
to  the  heat  represented  by  the  area  beneath  AB,  down  to 
absolute  zero  of  temperature,  minus  that  represented  by  the 
area  beneath  AEi.  Thus,  the  heat  liberated  from  the  water  = 
/f^  =  151.4 -(entropy  change  from  A  to  ^i)  X600  =  151.4 - 
(0.42-0.20)600  =  19.4  B.T.U.  per  pound. 

If  the  boiler  contained  40,000  pds.  of  water  and  450  cu.  ft. 
of  steam  at  57  lbs.  per  sq.  inch  the  weight  of  the  steam  present 
would  be  450-^7.45  =  60  pounds,  and  each  pound  would  liber- 
ate heat  represented  by  the  area  ABCEA,  or  202  B.T.U., 
approximately.  The  total  heat  liberated  by  60  poimds  steam 
would  be  60X202  =  12,120  B.T.U.,  or  9,420,000  ft.-pds. 

The  heat  liberated  by  the  water  would  be  40,000  X  19.4  = 
776,000  B.T.U.,  or  about  600,000,000  foot-pounds  of  energy. 


56  STEAM-TURBINES 

The  boiler  pressure  assumed  in  the  present  example  is 
from  one  third  to  one  quarter  of  that  commonly  carried  on 
boilers  of  the  Scotch  Marine  type,  but  it  gives  a  means  of  grasp- 
ing the  reason  for  the  disastrous  effects  of  a  boiler  explosion, 
where  the  contents  of  a  boiler  are  allowed  to  expand  instantly 
to  a  lower  pressure  and  temperature.  It  is  evident,  also, 
that  the  destructive  power  is  almost  wholly  due  to  the  large 
quantity  of  water  carried  in  the  boiler  and  not  to  the  steam 
present  at  any  one  time. 

(6)  Formation  and  adiahatic  expansion  of  steam. — If,  instead 
of  being  allowed  to  expand  from  B  to  E^,  the  water  were  evapo- 
rated into  steam  by  the  addition  of  heat  along  the  isothermal 
BC,  the  heat  necessary  to  entirely  evaporate  a  pound  of  water 
would  be  represented  by  the  area  beneath  the  line  BC,  and 
extending  down  to  the  absolute  zero  of  temperature.  The  total 
amount  of  heat  contained  by  the  pound  of  steam,  above  493 
degrees  absolute,  would  then  be  the  sum  of  the  heat  of  the 
liquid  and  that  of  vaporization,  or  258.6  +  (entropy  change 
from  B  to  C  X 750)  =  approximately  258.6  +  1.215x750  =  1169.6 
B.T.U. 

The  cycle  under  consideration,  however,  does  not  begin  at 
493  degrees  absolute,  but  at  600  degrees,  indicated  at  the  point 
A.  The  heat  that  has  been  added  to  that  possessed  by  the 
water  at  A  is 

H^+H,  =  151.4  + 1.215  X750  =  1062.4  B.T.U. 

This  is  the  heat  represented  by  the  area  beneath  the  broken 
line  ABC  down  to  absolute  zero  of  temperature. 

If,  now,  adiabatic  expansion  should  occur  down  the  line  CE, 
that  is  to  the  lowest  available  pressure  and  temperature  (that 
at  E),  the  heat  available  for  transformation  into  kinetic  energy 
would  be  that  represented  by  the  area  ABCE,  or 

19.4  +  entropy  change  along  BC  X  (750  -  600) 

=  19.4  +  1.215x150  =  201.7  B.T.U. 


WORK  DONE  IN  HEAT   TRANSFORMATIONS.  57 

The  heat  rejected  into  the  condenser  would  be  that  beneath 
the  Une  AE,  or 

Heat  rejected  =  change  of  entropy  along  ^4£'x600  =  (1.64— 0.20) 
X600  =  364  B.T.U.,  approximately. 

The  efficiency  of  the  cycle  is 

Heat  utilized      201.7 
Heat  supplied  ~  1062  ~^•^^• 

The  working  substance,  after  expansion  as  steam  followed 
by  condensation,  would  again  be  in  the  state  of  water,  repre- 
sented by  the  point  A,  and  would  be  ready  to  be  heated  again 
to  the  boiling-point,  evaporated,  and  carried  through  the  cycle 
of  operations  as  before. 

If  not  enough  heat  had  been  added  to  completely  evaporate 
the  water  into  dry  steam,  the  state  point  would  have  reached 
some  such  point  as  H,  and  the  quality  of  the  steam,  or  per- 
centage of  dry  steam  present,  would  have  been  equal  to  entropy 
BH  ^entropy  BC.  On  the  diagram  the  quahty  and  also  the 
heat  contents  above  493  degrees  absolute  can  be  found  by  inter- 
polation between  the  quality  curves  and  the  total  heat  curves 
respectively. 

(c)  Formation  and  expansion  of  superheated  steam. — After 
dry  steam  has  been  formed,  thereby  bringing  the  state  point 
to  C,  the  addition  of  further  heat  results  in  ''superheated 
steam,''  or  steam  having  a  higher  temperature  than  that  at 
which  it  was  generated,  and  corresponding  to  the  pressure  at 
which  it  exists. 

The  curves  for  constant-pressure  and  constant-heat  con- 
tents for  superheated  steam  have  been  explained. 

Suppose  heat  to  have  been  added  to  the  dry  steam  at  C 
until  the  temperature  rises  to  that  at  D,  or  920  degrees  absolute. 
It  has  been  shown  that  if  the  specific  heat  of  superheated 
steam  at  the  pressure  under  consideration  is  0.57,  the  heat 
necessary  to  raise  the  temperature  of  dry  steam  from  750  to 
920  degrees  will  be 

//« =0.57(920 -750)  =97  B.T.U. 


58  STEAM-TURBINES. 

The  total  heat  above  493  absolute  in  the  pound  of  steam  at 
D  is  approximately  258  +  911  +  97  =  1266  B.T.U.,  and  this  is 
represented  by  the  area  beneath  the  broken  line  XABCD 
down  to  absolute  zero  of  temperature. 

Suppose  the  pound  of  steam  to  expand  adiabatically  from 
D  to  the  condenser  temperature  and  pressure  at  E'.  The 
heat  in  the  steam  above  the  starting  temperature  at  A  is, 
approximately, 

i7r=  151+911+97  =  1159  B.T.U., 

and  this  is  represented  by  the  area  beneath  A  BCD  down  to 
absolute  zero.  But  only  the  heat  above  the  horizontal  line 
AE'  is  available  for  transformation  into  kinetic  energy,  and 
this  equals 

1159-  (change  of  entropy  along  AE')  X600 

=  1159-1.54x600=236  B.T.U. 

The  efficiency  of  the  ideal  cycle  is,  then,  236-^1159=0.204. 
It  is  evident  that  the  efficiency  of  the  ideal  cycle  is  not  greatly 
increased  by  adding  the  above  amount  of  superheat  to  steam  of 
the  low  pressure  assumed  in  the  example.  The  superheat 
would,  however,  decrease  the  losses  by  condensation,  friction  of 
steam,  etc.,  and  so  increase  the  efficiency  of  the  actual  cycle. 

It  is  to  be  noted  that  the  steam  would  remain  superheated 
during  expansion  until  reaching  the  point  S,  when  it  would 
become  just  dry  and  saturated.  Below  S  expansion  would 
cause  condensation,  and  at  E'  the  quality  of  the  steam  would 
be  represented  by  entropy  AE'  -^AF. 

(d)  Suppose  superheated  steam  at  D,  containing  1159  B.T.U. 
per  pound  above  the  starting-point  at  A,  to  expand  along 
some  path  such  as  DE" ,  instead  of  along  the  adiabatic  DE' ,  but 
falling  finally  to  the  same  lower  pressure  as  before  (note  that 
the  line  FE''  represents  the  same  pressure  as  does  the  horizontal 
AF).  The  position  of  the  point  E"  indicates  that  the  steam 
contains,  after  expansion  to  E",  1145  B.T.U.  per  pound,  above 


WORK  DONE  IN  HEAT   TRANSFORMATIONS.  59 

493  degrees  absolute.  Since  the  heat  of  the  hquid  at  A  is 
107  B.T.U.,  approximately  (from  the  steam-tables),  the  heat  at 
E"  above  that  at  A  is  1145-107  =  1038  B.T.U. 

The  steam  now  falls  in  temperature,  at  the  condenser  pres- 
sure, to  the  lowest  available  temperature,  that  at  F,  and  in  so 
doing  gives  up  the  heat  beneath  E''F,  which  equals  1145  — 1124  = 
21  B.T.U.  The  heat  at  F  above  that  at  A  then  equals  1038-21 
=  1017. 

Tne  total  heat  above  A  which  was  available  at  D  before 
expansion  was  1159  B.T.U.  Of  this,  1017  B.T.U.  are  to  be 
rejected,  and  the  heat  utilized  is  1159-1017  =  142  B.T.U. 

The  efficiency  of  the  cycle  is  142-^1159=0.129. 

The  falling  off  in  efficiency  is  due  to  the  fact  that  the  steam 
has  been  prevented  from  attaining  the  lower  temperature 
attained  after  adiabatic  expansion,  and  that  no  steam  has  been 
condensed  during  the  expansion.  Thus  it  contains,  at  the 
end  of  expansion  to  the  lowest  available  pressure,  a  very  much 
larger  amount  of  heat  than  it  contained  after  adiabatic  expansion 
to  E',  and  that  larger  amount  of  heat  has  to  be  rejected  to 
the  condenser.  The  conditions  tending  to  prevent  adiabatic 
expansion  will  be  taken  up  in  the  next  chapter. 

The  temperature-entropy  chart  at  the  back  of  the  book 
forms  a  graphical  steam-table,  calculated  by  means  of  the 
principles  stated  in  the  foregoing  pages. 

The  curve  marked  ''Pressure  and  Temperature  Curve" 
renders  it  possible  to  find  the  absolute  temperature  for  any 
of  the  absolute  pressures  at  the •  top  of  the  chart.  Having 
found  the  temperature  corresponding  to  any  pressure  the 
specific  volume  of  dry  steam  at  that  temperature  may  be 
found  from  the  terminations  of  the  constant-volume  lines  in 
the  dry-steam  line.  Thus,  let  it  be  required  to  find  the  abso- 
lute temperature  corresponding  to  120  pounds  absolute  pressure. 
Passing  down  the  line  marked  120  at  the  top  of  the  chart  until 
the  pressure-temperature  curve  is  reached,  the  intersection  is 
at  the  height  corresponding  to  802  degrees  absolute,  as  nearly 
as  can  be  read  on  the  chart.     By  consulting  steam-tables  the 


60  STEAM-TURBINES. 

figure  given  is  801.9  degrees.  For  finding  the  specific  volume 
(cubic  feet  per  pound  of  dry  saturated  steam)  the  fine  of  802 
degrees  intersects  the  saturation  curve  at  a  point  lying  between 
the  lines  of  constant  volume  for  3  and  4  cubic  feet.  The  short 
lines  intersecting  the  saturation  curve  mark  off  quarters  of 
cubic  feet  in  the  portion  of  the  chart  under  consideration.  At 
lower  temperatures  and  greater  specific  volumes  the  distances 
between  the  volume  curves  represent  greater  differences.  The 
intersection  giving  the  specific  volume  for  802  degrees  absolute 
is  just  above  the  line  marking  3.75  cubic  feet,  and  interpolation 
gives  about  3.7  cubic  feet  as  the  volume  required.  In  the 
steam-tables  the  volume  is  given  as  3.71  cubic  feet  per  pound. 
This  is,  of  course,  for  dry  steam  of  quality  100  per  cent.  If 
it  is  desired  to  know  the  specific  volume  for  any  other  quality 
of  steam,  it  is  simply  necessary  to  find  the  intersection  of  the 
same  temperature  line  with  the  quality  line  desired,  and  to 
interpolate  between  the  volume  lines  for  the  specific  volume. 
Suppose  the  specific  volume  of  steam  of  120  pounds  absolute 
and  95  per  cent  quafity  is  desired  to  be  known.  Passing  to 
the  left  from  the  saturation  curve  along  the  line  of  802  degrees 
absolute,  until  a  point  is  reached  half-way  between  the  curves 
of  90  and  100  per  cent  quality,  the  specific  volume  is  found 
to  be  3.5  cubic  feet. 

While  the  temperature-entropy  form  of  heat-diagram  is 
most  admirably  adapted  to  the  graphical  illustration  of  heat 
changes,  and  of  thermodynamic  problems  in  general,  and  should 
be  thoroughly  studied  by  the  student,  the  diagram  proposed 
by  Dr.  Mollier  having  temperature  as  ordinates  and  thermal 
units  as  abscissae  is  more  readily  used  in  the  solution  of  such 
problems  as  come  to  the  engineer.  The  Mollier  diagram  at 
the  back  of  the  book  will  be  found  to  facilitate  the  problem 
work  called  for  in  the  following  chapters. 


CHAPTER  IV. 

CALCULATION  OF  VELOCITY  AND  WEIGHT  OF  FLOW. 

By  means  of  the  principles  stated  in  Chapters  II  and  III, 
the  heat  drop  accompanying  the  expansion  of  steam  may  be 
calculated,  and  from  this  may  be  found  the  steam  velocity 
that  would  result  if  all  the  heat  given  up  during  expansion  were 
reahzed  as  kinetic  energy  in  the  jet  of  steam.  It  was  shown 
in  Chapter  II  that  if  Hi  and  H2  represent  respectively  the 
heat  contents  of  the  steam,  per  pound,  before  and  after  expan- 
sion through  an  orifice  or  a  nozzle,  the  velocity  equation  may 
be  written 

^  =  778(^1-^2) (11) 

The  velocity  of  flow  may  be  calculated  from  the  following 
equations : 

Let  qi  and  qo  represent  the  heat  of  the  liquid  at  the  higher 
and  lower  temperatures,  respectively. 

Let  E  represent  entropy  changes  as  marked  on  Fig.  21  and 
indicated  by  the  subscripts  used  with  the  letter  E. 

Let  H^  represent  the  heat  of  vaporization  present  in  steam 
of  quality  x==l. 

Let  Ti  and  T2  represent  absolute  temperatures  of  dry 
saturated  steam  at  boiler  pressure  and  exliaust  at  condenser 
pressure,  respectively. 

61 


62 


STEAM-TURBINES. 


Let  7^3  represent  the  absolute  temperature  to  which  the 

«team  is  superheated. 

For  moist  steam  (of  quality  =  x),  or  dry  steam  (of  quality 

x  =  l) 

72 

nS{qi-q2-VxH^-T2{EyYxE^-E2)\.  ,     .     (12) 


2^ 
For  superheated  steam,  calUng  the  specific  heat  S, 


V2 


^j  =  77^^q,-q2+H,  +  S{T^-T{) 

-T2{E,+E,+S\og^'^-E^\.     (13) 


T 


-X^-, 


—> 


E^+  xE,,-Et 


-Ei+E„-E5- 


FiG.  21. 


Experimental  and  mathematical  investigations  indicate  in 
general  that  the  pressure  within  an  orifice  through  which  steam 
is  flowing  does  not  fall  below  about  0.57  or  0.58  of  the  initial 
absolute  pressure.  It  seems  that  the  pressure  falls  to  a  value 
corresponding  to  the  heat  conversion  that  will  give  to  the  steam 


CALCULATION  OF   VELOCITY  AND    WEIGHT  OF  FLOW.     6S 

immediately  in  the  narrowest  section  of  the  orifice  a  velocity 
about  the  same  as  tliat  of  the  disturbance  called  "sound," 
or  about  1400  or  1500  feet  per  second.*  Any  farther  fall  in 
pressure  and  temperature  must  take  place  beyond  the  narrowest 
section,  but  the  velocity  attained  in  the  narrowest  section 
determines  the  weight  of  flow,  per  unit  of  time,  that  it  is 
possible  for  a  given  initial  pressure  to  produce. 

The  general  explanation  of  this  phenomenon  is  found  in 
the  development  of  Zeuner's  equation  given  on  pages  36  and 
37,  which  indicates  that  for  any  fluid  flowing  through  an  orifice, 
the  fall  of  pressure  immediately  in  the  orifice  is  limited  to  a 
fraction  of  the  initial  pressure  depending  for  its  value  upon 
the  ratio  of  the  specific  heats  of  the  substance  at  constant 
pressure  and  at  constant  volume,  respectively.  In  the  case  of 
steam  the  pressure  falls  to  that  value  which  gives  the  maxi- 
mum possible  flow,  by  weight,  and  does  not  fall  below  this 
pressure  until  after  the  steam  leaves  the  smallest  portion  of 
the  orifice.  The  maximum  flow  from  a  nozzle  leading  from 
a  simple  orifice  may  occur  when  the  exit  or  ''back"  pressure 
is  higher  than  0.57pi,  as  shown  on  Plates  IV,  V,  and  VI;  but 
in  these  cases  the  pressure  in  the  orifice  is  lower  than  that 
at  exit  from  the  nozzle  (see  Fig.  53),  and  the  fall  of  pressure 
in  the  throat  determines  the  weight  of  flow.  It  is  to  be  noted 
in  this  connection  that  the  limiting  velocity  of  1400  to  1500 
feet  per  second  applies  to  only  the  narrowest  portion  of  the 
nozzle,  and  that  farther  fall  in  pressure  beyond  this  point  may 
very  considerably  increase  the  velocity  of  the  stream. 

Referring  to  Plates  IV,  V,  and  VI,  curves  No.  2  show  experi- 
mentally determined  weights  per  second  flowing  from  orifice 
No.  2,  the  entrance  to  which  is  rounded.  Assuming  that  in  each 
case  the  orifice  pressure  is  0.57  of  the  initial  pressure  when  the 
maximum  weight  of  steam  flows  through  the  orifice,  calculations 
according  to  the  equation  on  page  62  for  moist  and  for  dry 
steam  give  the  following  results: 

*  The  rate  of  wave  propagation  depending  upon  the  temperature  in  tlie 
orifice.  See  "Outflow  Phenomena  of  Steam."  Paul  Euiden.  Munich,  1908^ 
Ii.  OMenbourg. 


64 


STEAM-TURBINES. 
Table  No.  1. 


Initial  Pres- 

Weight  of  Flow,  Pounds  per  Second. 

Calculated 

eure,  Pounds 

Ab.solute 
per  Square 

Orifice 

Pressure. 

P2  =  0.57Pi. 

Observed. 

Calculated 

\elocity,  Feet 
per  Second 
at  Smallest 

Inch. 
-Pi 

By  Equation 
Given. 

By  Napier's 
Formula. 

Cross-section 
of  Orifice. 

132.3 
117.6 
102.9 

75.2 
67.0 

58.7 

0.063 
0.057 
0.050 

0.0629 
0.0572 
0.0500 

0.0671 
0.0.596 
0.0522 

1470 
1495 
1490 

The  experiments  upon  which  the  above  table  and  the  curves 
on  Plates  IV,  Y,  and  YI  are  based  were  made  by  Professor 
Gutermuth,  of  Darmstadt,  and  were  published  in  the  Zeit- 
schrift  des  Yereines  Deutscher  Ingenieure,  Jan.  16,  1904. 

The  following  specimen  calculation  shows  the  method  of 
using  the  equations  on  page  62.  Taking  the  conditions  in  the 
first  case  in  the  above  table. 


gi+i7„  =  1188B.T.U.; 


Pi  =  132.3  pds.  absolute  per  sq.  inch; 

qi  =heat  of  liquid  at  Pi  =319.3  B.T.U.  1 
H^=   "     "  vaporization  at  Pi  =  868.4    J 
Ei+E  =. specific  entropy  of  steam  at  Pi  =  1.573; 
p2  =  pressure  in  the  orifice,  pds.  abs.  per  sq.  inch  =  75.2  pounds; 

g'2=heat  of  liqu  d  at  P2  =  277  B.T.U.; 
T2  =  absolute  temperature  at  P2  =  768°  F. ; 
£"2  =  specific  entropy  of  water  at  P2  =  0.446; 
Specific  volume  of  dry  steam  at  P2  =  5.75  cu.  ft. 

From  equation  (12j,  for  moist  or  dry  steam,  on  page  62, 

V'~-^2g  =  778(q,-q2+H,-T2(E,+E,-E2)), 
f:ora  which  7  =  1470  ft.  per  second. 

Calculating  the  quahty  of  steam  after  expanding  adiabatic- 
ally  from  132.3  to  75.2  pounds  absolute,  the  specific  volume 
at  the  lower  pressure  will  be  0.965x5.75  =  5.55  cu.  ft. 

The  steam  flows  through  an  orifice  of  0.0355  in.  cross-sec- 
tional area  at  the  velocity  1470  f  .  per  second. 


CALCULATION  OF  VELOCITY  AND  WEIGHT  OF  FLOW.     65 

Since  for  steady  flow 

Volume  discharged  =  area  of  orifice  X  velocity, 

the  volume  flowing  per  second  =  0.0355  -^  144  X 1470  =  0.362  cu.  ft., 
and  since  each  cubic  foot  weighs  -^-j?  pounds,  the  weight  flowing 

0.362 
per  second  is   _  „-  =  0.0629  pounds, 
o.  ( o 

The  calculation  for  the  weight    of  flow  through  an  orifice 

may  be  simplified  by  an  approximation  to  the  area  of  the  heat 

diagram,  as  follows: 

HN 

Assummg  that  steam  of  quality  jfTf  expands  adiabatically 

along  the  line  NA  (Fig.  22),  the  heat  given  up  is  represented  by 


Fig.  22. 


the  area  FHXAF  lymg  between  the  limits  of  temperature  Ti 
and  T2.  This  area  is  equal  to  the  mean  width  of  the  area  mul- 
tiphed  by  the  range   of  temperature,  or  since  FH  is  nearly 


66  STEAM-TURBINES. 

a  straight  line,   the   heat  causing  flow  =  X(7'i —7'2)=  approxi- 
mately 

(entropy  giV  + entropy  FA)^^ 
2  ^^  1  —  J  2;. 

Taking  the  data  in  the  second  line  of  the  table  on  page  64, 

Pi  =117.6  pds.  abs. 

7^1=800  degs.  abs. 

P2  =  pressure  in  orifice,  or  0.57Pi  =67  pds. 

T'2  =  761  degs.  abs. 

Assume  that  the  quality  of  the  entering  steam  is  100%  or 
that  N  coincides  with  M,  then 

Entropy  FiV  =1.093 

Entropy  FA  =0.053  + 1.093  =  1.146 


Entropy  HN+FA  =2.239 

2  239 

-^ —  =  1.12  entropy  corresponding  to  mean  ordinate. 

800-761=39  degs. 
39X1.12=43.6  B.T.U. 


Velocity  =\/778x43.6x64.4  =  1480  ft.  per  second. 

The  velocity  calculated  on  page  64  is  1495  feet  per  second. 
The  specific  volume  of  steam  at  the  orifice  pressure  of  67  pds. 
is  6.4  cu.  ft.     Cross-sectional  area  is  0.0355  sq.  inch. 

The  weight  flowing  per  second  is  then 

0.0355X1480 


144X6.4 


=  0.057  pound. 


Let  area  of  orifice  in  sq.  inches  be  called  A  ; 

specific  volume  (cu.  ft.  per  pound)  of  steam  after  expand- 
ing to  P2  (=0.57Pi)  be  called  V2; 
entropy  values   be  designated  by  letter  E  with  sub- 
scripts, that  is,  as  Ei  and  E2,  Fig.  22. 
temperatures  corresponding  to  Pi  and  0.57  Pi  be  called  Ti 
and  T2  respectively. 


CALCULATION  OF  VELOCITY  AND  WEIGHT  OF  FLOW.     67 
The  weight  flowing  per  second  = 

^hl^V(E,+E2)(T,-T2) (14) 

The  formula  may  be  extended  so  as  to  include  cases  in  which 
superheated  steam  is  used,  by  adding  to  the  expression  under 
the  radical  the  equivalent  of  the  superheat  in  the  steam  per 
pound. 

The  volume  I'o  afcer  expansion  to  0.57Pi  will  be  very  nearly 
96  5%  of  the  specific  voluiiic  at  the  pressure  O.oTPi.  This 
maj^  be  verified  by  means  of  the  heat  diagram  by  finding 
the  quality  of  steam  after  the  expansion  stated. 

Calculation  of  Rate  of  Flow  and  of  Reaction  against  the  Out- 
flow Vessel.— If  the  reaction  due  to  a  jet  delivering  a  given 
weight  of  substance  per  unit  of  time  be  known  the  velocity 
of  the  jet  can  be  computed. 

The  velocity  of  a  jet  is  produced  by  a  force  urging  the  sub- 
stance onward,  and  the  work  done  by  this  force  is  the  equivalent 
of  the  heat  given  up  by  the  steam  during  its  fall  in  pressure 
and  temperature  as  it  flows  through  the  orifice,  or  nozzle. 

Nature  of  the  Reaction. — A  jet  in  flowing  from  an  orifice 
in  a  chamber  suspended  by  a  flexible  tube  as  in  Fig.  23, 
causes  the  chamber  from  which  the  jet  flows  to  move  in  a 
direction  opposite  to  that  of  the  flow  of  steam,  and  to  assume 
some  new  position,  as  indicated  by  the  dotted  lines.  While 
the  force  holding  the  chamber  in  this  new  position  is  the  equiv- 
alent of  the  force  urging  the  jet  onward,  and  may  therefore 
be  used  as  such  in  computing  the  velocity  of  the  jet,  the  true 
nature  of  the  influence  producing  the  reaction  is  not  brought 
out  l)y  such  an  explanation. 

If  a  force  could  be  conceived  to  act  back  through  the  stream 
and  thus  push  the  chamber  into  the  new  position,  it  would  be 
necessary  to  conceive  also  of  a  point  of  application  of  the  force 


68 


STEAM-TURBINES. 


to  the  object  moved — that  is,  to  the  chamber  from  which  the 
jet  flows.  If  the  force  were  apphed  to  the  steam  within  the 
chamber,  the  unit  pressure  within  would  be  increased.  This 
is  contrary  to  observation,  and,  besides,  such  an  increase  in 
pressure  would  apply  to  all  sides  of  the  chamber,  and  no  un- 


FiG.  23. 


balanced  forces  would  arise  to  cause  displacement  of  the  chamber 
as  a  whole. 

It  would  be  difficult  to  conceive  of  a  force  acting  in  a  direc- 
tion opposite  to  that  of  the  flow  of  steam,  and  being  applied 
to  the  edges  of  the  orifice  in  such  a  way  as  to  affect  the  position 
of  the  chamber. 


CALCULATION  OF   VELOCITY  AND  WEIGHT  OF  FLOW.     69 

Without  speculating  further,  the  removal  of  pressure  at  the 
entrance  to  the  orifice  allows  the  steam  about  the  entrance  to 
expand  in  volume,  to  fall  in  pressure  and  temperature,  and  to 
be  forced  through  the  orifice  by  that  part  of  the  intrinsic  energy 
of  the  steam  itself  which  is  given  up  during  the  expansion,  and 
converted  into  the  kinetic  energy  of  flow.  The  diminution  of 
pressure  about  the  entrance  to  the  orifice  while  the  pressure  on 
the  other  surfaces  of  the  interior  of  the  chamber  remains  the 
same  as  before  results  in  an  unbalanced  force  wdthin  the  vessel, 
causing  displacement  of  the  vessel  as  a  whole.  Equilibrium  is 
restored  only  when  the  elasticity  of  the  supporting  tube  causes 
a  force  sufficient  to  balance  the  resultant  of  the  internal  pres- 
sures.* 

If  a  conically  divergent  nozzle  of  suitable  proportions  be 
added  to  the  orifice  on  the  side  of  the  chamber,  the  expan- 
sion of  the  steam  after  it  leaves  the  orifice  may,  witli  cer- 
tain initial  pressures,  result  in  a  higher  velocity  of  flow  in  a 
given  direction  than  occurs  after  expansion  through  a  simple 
orifice.  If  the  steam,  before  lea\'ing  the  large  end  of  the  nozzle, 
expands  down  to  the  external  pressure  at  the  exit  from  the 
nozzle,  then  the  velocity  of  flow  will  be  as  great  as  it  is  pos- 
sible to  attain  with  the  pressures  involved  and  the  particular 
nozzle  in  question. 

The  question  arises,  since  an  increase  in  velocity  must  be 
accompanied  by  an  increased  reaction,  where  does  the  addi- 
tional unbalanced  force  find  its  point  of  application?  Assum- 
ing that  for  a  given  nozzle  and  given  initial  pressure  definite 
orifice  conditions  exist  as  to  pressure  and  rate  of  flow,  the 
conditions  of  expansion  in  the  part  of  the  nozzle  beyond  the 
orifice  may  be  supposed  to  not  affect  the  orifice  conditions. 
Taking  two  sections  indefinitely  near  to  each  other,  at  which 
pressures  p  and  (p  —  dp)  exist,  a  pressure  p'  acts  in  the  chrec- 
tion  AC,  normal  to  the  nozzle  surface,  upon  each  elementary 
area,  and  may  be  resolved  into  two  components,  AB  and  BC, 
perpendicular  and  parallel,  respectively,  to  the  direction  of  flow. 
If  the  nozzle  sides  make  an  angle  a  with  the  direction  of  flow 

*  Neglecting  the  weight  of  the  parts. 


70 


STEAM-TURBINES. 


the  components  along  and  perpendicular,  respectively,  to  that 
direction  are  (Fig.  24) : 

BC  =  p'  sin  a, 

AB=p'  cos  a. 

If  the  rate  of  pressure  fall  along  the  nozzle  be  assumed, 
the  integration  of  the  above  expressions  over  the  interior  sur- 
face of  the  nozzle  will  give  values  for  the  components  AB 
and  BC,  the  latter  representing  the  reaction  against  the  nozzle. 
Further  analysis  would  not  assist  in  the  following  application 
of  the  reaction  principle  to  problems  in  the  flow  of  steam, 
since  the  pressures  in  the  nozzle  vary  in  a  complex  manner; 


Fig.  24. 

but  the  above  indicates  the  general  character  of  the  forces 
involved.  It  is  evident  that  the  reaction  accompanying  flow 
through  a  straight  nozzle  or  pipe  would  not  differ  from  that 
through  a  simple  orifice,  except  that  the  rate  of  flow  would 
be  affected  by  the  friction  caused  by  the  nozzle  walls. 

The  development  of  ecjuation  14  shows  that  the  maximum 
possible  velocity  due  to  adiabatic  expansion  from  Pi  to  P2  is, 
approximately, 


=  158\/{Ei+E2){Ti-T2),       .     .     .     (15) 

where   Ei   and   E2   represent   entropy  changes,  as  stated   on 
page  66. 


CALCULATION  OF  VELOCITY  AND   WEIGHT  OF  FLOW.     71 

If  the  expansion  is  that  occurring  in  an  orifice,  the  range 
of  pressures  is  between  Pi  and  0.57Pi,  and  at  the  higher  pres- 
sures, that  is  between  200  pounds  and  100  pounds,  the  value 
of  the  expression  under  the  radical  is  from  9.60  to  9.70. 
Below  100  pounds  the  value  is  from  9.0  to  9.4.  Taking  an 
average  value  of  9.5,  the  hmiting  velocity  in  the  plane  of  an 
orifice  is,  approximately, 

158X9.5  =  1500  ft.  per  sec. 

The  weight  of  flow  may  be  calculated  by  using  the  follow- 
ing formula: 

AV2 


W  = 


V2XI44' 


where    A  =  area  of  orifice  in  square  inches; 

F2  =  1450  for  initial  pressures  below  100  pds.  abs.; 
F2  =  1520  for  initial  pressures  above  100  pds.  abs.; 
?;2  =  cubic  ft.  per  pound  at  pres.  of  P2  =  0.57Pi. 

For  example, 

Let  Pi  =  155   pounds  per  sq.   inch   absolute.    Then  P2  = 
0.57X160  =  88  pounds. 
1-2  =  4.96. 
Let  .4  =0.0275  sq.  in. 

,xr  •  1.  1     0.0275X1520    ^  ^_, 

Weight  per  second  =  -^r7  .      .  , ,     =  O.O080. 
144X4.96 

This  result  may  be  compared  with  the  result  for  155  pounds 
pressure  on  page  92. 

A  more  satisfactory  formula,  however,  is  derived  from 
the  velocity  as  given  on  the  preceding  page,  as  follows: 

V  =  15SV{Ei+E2){Ti-T2), 

W==l^V{Ei+E2){Ti-T2), 
144i'2 

V2 


72  STEAM-TURBINES. 

This  will  be  found  to  give  results  agreeing  very  closely  with 
the  actual  weight  of  flow  from  orifices  with  rounded  entrance. 
The  statement  is  frequently  made  and  seems  to  have  been 
largely  accepted,  that  steam  flowing  through  a  simple  orifice 
cannot  attain  a  velocity  greater  than  about  1500  feet  per 
second.  This  is  probably  true  for  the  position  immediately 
at  the  smallest  section  through  which  the  steam  passes,  but 
it  should  not  therefrom  be  concluded  that  the  total  kinetic 
energy  possessed  by  a  jet  from  an  orifice  is  limited  to  the  amount 
corresponding  to  that  velocity.  It  seems  that  in  flowing 
through  a  simple  orifice  steam  gives  up  energy  until  it  attains 
a  velocity  corresponding  to  about  that  stated,  but  that  after 
that  state  of  activity  has  been  reached,  further  acceleration 
does  not  occur  until  the  narrowest  section  has  been  passed. 
As  soon  as  the  steam  reaches  a  point  just  beyond  that  section, 
however,  it  is  free  to  expand  to  the  pressure  of  the  medium  into 
which  the  orifice  leads.  The  jet  issues  in  a  well-formed  stream 
in  a  given  direction,  and  as  it  falls  in  temperature  the  heat 
liberated  tends  to  further  accelerate  the  jet  in  the  direction 
of  motion.  If  there  is  no  directing  nozzle  beyond  the  orifice, 
however,  the  jet  begins  to  spread  soon  after  leaving  the  orifice, 
and  hence  its  kinetic  energy  is  given  up  in  directions  other 
than  that  of  the  original  jet.  The  same  amount  of  energy 
is  given  up  by  a  jet  from  an  orifice  as  from  an  expanding  nozzle, 
but  the  latter,  if  properly  proportioned,  serves  to  contain  the 
steam  during  expansion  so  that  the  maximum  possible  velocity 
in  a  given  direction  is  obtained  with  little  vibration  of  the 
atmosphere  and  consequent  loss  of  energy. 

The  experimental  work  discussed  in  Ch.  \T  indicates  that 
much  higher  velocities  than  ordinarily  supposed  are  possible 
by  the  use  of  orifices,  and  it  has  been  found  in  building  certain 
turbines  of  the  impulse  type  that  fully  as  good,  if  not  better, 
results  are  obtained  in  the  lower  stages  of  turbines  by  the  use 
of  orifices  instead  of  nozzles.  The  latter  are  especially  suited 
to  pressures  above  70  or  80  pounds  absolute. 

In  the  ideal  case,  used  for  predicting  results  to  be  expected, 


CALCULATION  OF   VELOCITY  AND   WEIGHT  OF  FLOW.     73 

the    following   tste}).s    may   be    taken    towards   calculating   the 
weight  of  flow  and  A'clocity. 

(a)  Find  the  weight  of  flow  caused  by  the  fall  in  pressure 
in  the  orifice  to  0.57Pi,  as  in  the  equation 

W  =^V(Ei+E2KTi-T2). 

(b)  Find  the  velocity  corresponding  to  the  heat  given  up 
during  drop  in  pressure  to  that  existing  at  the  exit  of  the  orifice 
or  nozzle,  or  Ps,  from  equation  (15) : 


y  =  158\/(^i+^3)(7^i-7^3), 

where  E^  is  the  entropy  change  (marked  Ej  on  the  diagram 
Fig.  22),  and  7^3  is  the  corresponding  absolute  temperature. 

(c)  Correct  these  by  experimentally  determined  coefficients 
for  friction  and  other  losses,  as  will  be  explained  in  the  following 
chapter. 

(d)  If  the  weight  of  steam  flowing  through  the  passageway 
per  unit  of  time  has  been  determined  experimentally,  or  if  the 
reaction  has  been  so  found,  it  may  be  useful  to  employ  these 
values  for  calculating  the  actual  velocity. 

The  reaction  in  pounds  has  been  shown  to  equal  the  weight 
of  flow  per  second  times  velocity  in  feet  per  second  divided 
'^y  fJ  (=32.2).  The  equation  for  calculating  the  reaction  may 
be  written 

R  =  ^='^^\(Ei  +  Es){T^-Ts)\iX^'^{(E,  +  E2)iT,-T2)\i 
=  ^{(E,+Es)iE,+E2)(Ti-Ts)iT,-T2)]K        (16) 

V2 

In  the  above,  .4.=  area  of  least  cross-section  of  passage,  in 
square  inches. 

V2  =  specific  volume  of  steam  at  O.oTPi,  in  cubic  feet. 

Values  of  r,  E,  and  T  may  all  be  taken  from  the  heat  dia- 
gram directly,  with  sufficient  accuracy  for  engineering  pur- 
poses. 


74  STEAM-TURBINES. 

An  equation  for  calculating  the  reaction  of  a  jet  of  steam 
flowing  into  the  atmosphere  was  developed  about  the  time  when 
Mr.  George  Wilson's  experiments  were  made  (1872),  and  al- 
though the  equation  must  be  regarded  as  empirical,  it  expresses 
with  remarkable  closeness  the  results  that  have  been  obtained 
as  to  the  reaction  of  steam-jets  discharging  into  the  atmos- 
phere. The  reasoning  made  use  of  in  developing  the  equation 
was  somewhat  as  follows: 

If  steam  be  allowed  to  expand  behind  a  piston  in  a  cylinder 
from  Pi  to  0.57Pi,  adiabatically,  the  mean  effective  pres  ure 
will  be  about  0.33Pi.  If  a  stream  capable  of  exerting  this  mean 
pressure  were  allowed  to  flow  through  an  orifice,  it  would  be 
able,  according  to  the  principles  governing  the  impulse  of  jets 
of  fluid,  to  exert  an  impulsive  pressure,  and  therefore  a  reac- 
tion, of  twice  the  pressure  corresponding  to  its  static  head,  or 
of  O.66P1.  Besides  this  pressure  the  reaction  would  be  in- 
creased by  the  addition  of  the  pressure  in  the  orifice,  or  0.57Pi, 
but  as  the  flow  is  into  the  atmosphere,  and  Pi  is  in  pounds 
absolute,  the  atmospheric  pressure  must  be  subtracted.  The 
expression  for  the  reaction  then  becomes 

i^  =  Pi(0.66  +  0.57)-14.7  =  1.23Pi-14.71bs.  per  sq.  in.  of  orifice. 

The  following  table  *  shows  the  degree  of  approximation  to 
experimentally  determined  reactions  which  can  be  attained  by 
use  of  the  equation.  The  experiments  were  made  by  Mr.  George 
Wilson  with  the  apj^aratus  shown  on  page  140. 

Further  calculations  by  means  of  the  formula  just  developed 
are  given  in  Chapter  VI.  If  it  ])e  attempted  to  apply  the 
formula  to  cases  of  discharge  into  a  condenser  maintaining 
conditions  of  partial  vacuum,  it  will  appear  that  the  results 
are  not  in  accordance  with  calculations  made  on  the  basis  of 
heat  given  up.  The  maximum  velocity  of  flow  of  a  jet  dis- 
charging into  a  perfect  vacuum  would  l^e,  from  the  formula, 
that  corresponding  to  a  reaction  of  1.23Pi.      For  steam  of  an 

*  Proceedings  of  Engineers  and  Shipbuilders  of  Scotland,  1S74-5 


CALCULATION  OF  VELOCITY  AND   WEIGHT  OF  FLOW.     75 


Absolute  Pressure. 

Reaction,  Orifice 

Calculated 

Pounds  per 

1.0956  Sq.  Ins.  Area, 

Reaction  Calculated. 

Square  Inch. 

by  Experiment. 

Experimental 

16.49 

3.54 

3.63 

1.025 

18.10 

6.52 

6.78 

1.040 

19.98 

9.86 

10.05 

1.019 

23.10 

14.75 

14.92 

1.011 

24.  So 

17.27 

17.37 

1.005 

25.60 

18.32 

18.10 

0.988 

27.30 

20.84 

20 .  68 

0.992 

39.40 

38.00 

37.00 

0.973 

54.40 

59.00 

59.00 

1.000 

73.20 

85.11 

Reaction,  Orifice 

0.4869  Sq.  In.  Area. 

82.60 

0.970 

22.80 

8.10 

8.21 

1.013 

42.20 

18.22 

18.14 

0.995 

65.40 

32.50 

32.04 

0.986 

77.00 

39.55 

38.51 

0.973 

84.90 

44.00 

43.72 

0.994 

93.00 

48.50 

48.5.8 

1.002 

112.70 

58.30 

60.38 

1.034 

55.70 

26.67 

26.20 

0.983 

84.70 

44.30 

43 .  56 

0.983 

113.70 

59.60 
Sum 

60.90 

1.022 

...     20 . 008 

Average  of  20 

experiment  .s 

...       1.0004 

initial  pressure  of  160  pounds  absolute  per  sq.  in.,  discharging 
into  a  vacuum  of  28  ins.  tlirough  an  orifice  of  0.25  sq.  in.  cross- 
sectional  area,  the  maximum  weight  of  flow  per  second  would 
be 

1.1X0.25 


TT'  =  ^-^^^-V2.15X42  =  0.55  pds. 
The  reaction  would  be,  by  the  above  equation, 

7?  =  (1.23X160-1.0)0.25  =  49  pounds, 

and  the  velocity 

RO    49X32.2 
r  =TT^=  — TTT^ — =28/0  it.  per  second. 
It  O.oo  '■ 

This  result  may  be  compared  with  that  obtained  by  use  of 


76  STEAM-TURBINES. 

the  approximation  to  the  fundamental  equation  for  velocity, 
eq.  (15).    If  complete  expansion  occurs,  in  a  suitable  nozzle, 


7  =  158\/(^i  +  ^3)(^i-7^3) 
=  158  X  25.5  =  4030  ft.  per  second. 

It  will  be  shown  in  the  following  chapter  how  calculations 
made  by  the  last  used  equation  may  be  modified  by  a  suitable 
coefficient  for  friction  losses  in  the  nozzle  or  orifice,  so  as  to 
predict  results  to  be  expected  in  practice. 


CHAPTER  V. 

VELOCITY  AS  AFFECTED   BY  FRICTIONAL  RESISTANCES. 

Referring  to  Fig.  25,  let  a  pound  of  steam  be  at  pressure 
Pi  and  volume  Vi,  and  let  its  adiabatic  expansion  be  indicated 
by  curve  pii'i  —  p2^'2-     At  P2V2  partial  condensation  of  the  pound 


Fig.  25. 

of  steam  has  occurred,  and  there  exists  a  volume  V2  of  steam, 

and  a  certain  amount  of  water,  the  steam  and  water  together 

weighing  one  pound.     If  the  steam  contained  at  piVi  the  heat 

Hi,  and  contains  at  P2V2  the  heat  H2,  the  increase  of  velocity 

of  the  steam  that  could  occur,  due  to  the  fall  from  piVi  to 

P2V2,  is 

72  =  164.4X778  X(i/i-i/2)l*. 

77 


78  STEAM-TURBINES. 

Now  let  the  pound  of  steam  expand  from  the  same  initial 
condition  piVi  to  P2V3,  in  which  1-3  is  greater  than  V2.  Since 
the  final  pressure  p2  is  the  same  for  both  cases  of  expansion, 
the  steam  at  the  condition  of  greater  volume  per  pound,  V3, 
is  more  nearly  dry  than  at  V2.  This  means  that  after  expansion 
to  i'3  the  steam  possesses  more  energy  than  after  expansion 
to  V2,  or,  in  other  words,  it  has  given  up  less  of  its  energy  than 
was  given  up  by  expanding  adiabatically.  Ha\dng  reached  the 
lowest  available  pressure  and  temperature  at  p2,  the  steam 
cannot  give  up  any  further  energy,  because  it  cannot  fall  any 
further  in  temperature.  The  shaded  area  (Fig.  25)  represents 
the  difference  between  the  energy  (in  foot-pounds)  given  up 
by  the  steam  in  the  two  cases.  Let  the  quantity  of  heat  remain- 
ing in  the  steam  at  p2i'3  be  H2.  This  is  greater  than  H2  be- 
cause less  condensation  has  occurred  during  the  fall  from  piVi 
than  occurred  during  adiabatic  expansion. 

The  velocity  of  the  steam  after  falling  to  P2V3  is 

TV  =  {64.4  X778  X  {Hi  -H.')  ]K 

The  velocity  after  adiabatic  expansion  to  P2V2  is 

V2=  {Q4Ax778x(Hi-H2)]K 

The  difference  between   the  squares  of  the  velocities,  or  the 
loss  of  energy,  is  evidently  represented  by 

7^2  -  72'2  =  TV  =  1 64.4  X  778  X  (^2'  --^"2) } . 

Remembering   that   the   quantity   of   steam   involved   is   one 
pound,  the  loss  of  energy  is 


^'  =  778(^2' -i72). 


VELOCITY  AND  FRICTIOXAL  RESISTANCES. 


19 


Let  A^  Fig.  28,  represent  the  initial  condition  of  the  pound  of 
steam  (at  p^vi  in  the  pressure-volume  diagram),  and  let 
expansion  occur  adiabatically  along  NA  to  the  temperature 
corresponding  to  p2-  The  amount  of  steam  present  at  A  will 
be  FA-^FL  pounds,  and  the  amount  of  water  will  be  1—FA-^ 
FL  pounds.  The  quality  of  the  steam  will  therefore  be 
x^FA^FL.    If  expansion  occurs  in  a  passage  which  opposes 


frictional  resistance  to  the  flow,  the  steam  gives  up  part  of 
its  energy  to  overcome  the  resistance,  and  the  work  thus  done 
appears  as  heat  in  the  walls  of  the  passageway,  or  in  the  particles 
of  the  steam  itself.  Each  indefinitely  small  drop  in  tempera- 
ture is -accompanied  by  this  giving  up  of  heat  to  the  sm-round- 
ings  of  the  steam,  and  the  surroundings  give  back  heat  to  the 
steam  as  soon  as  the  latter  falls  below  the  temperature  to  which 
the  surroundings  have  been  heated.  This  giving  back  of  heat 
to  the  steam  re-evaporates  the  water  of  condensation  resulting 
from  adiabatic  expansion  and  raises  the  quality  of  the  steam 
so  that  expansion  occurs  along  some  such  line  as  XX.  If 
expansion  occurs  through  a  small  hole  into  a  comparatively 


80  STEAM-TURBINES. 

large  chamber,  as  in  a  throttling  calorimeter,  the  final  velocity 
of  the  steam  is  negligibly  small,  and  the  work  of  friction  is  all 
spent  in  increasing  the  internal  energy  of  the  steam  during 
its  fall  in  temperature.  Thus,  as  practically  no  heat  escapes, 
the  expansion  follows  the  constant  heat  curve  1".  At  any 
lower  temperature,  as  at  FL,  the  quantity  of  heat  present  is 
the  same  as  was  present  at  N,  but  no  external  work  has  been 
done;  and  if  FL  is  at  the  lowest  available  temperature,  the 
whole  of  the  heat  must  be  rejected  and  cannot  be  u&efuUy 
employed.  The  case  is  like  that  of  the  water  in  the  tail-race 
of  a  mill — it  can  fall  no  farther  and  hence  can  give  up  no  more 
energy,  although  the  mass  of  water  present  is  the  same  as  it 
was  as  it  flowed  in  the  penstock.  The  total  heat  above  the 
starting-point  F  in  a  pound  of  steam  at  condition  N,  Fig.  23,  is 

Hi^aresiGFHNADG. 

If  unresisted  adiabatic  expansion  occurs  along  NA,  the  quantity 
of  heat  usefully  employed  in  giving  velocity  to  the  steam  will  be 
that  represented  by  area  FHNAF. 

The  heat  rejected  along  the  hne  AF  of  lowest  available 
temperature  will  be 

H2  =  avea.GFADG. 

If  the  work  of  friction  in  the  nozzle  should  be  sufficient  to  cause 
the  steam  to  fall  in  temperature  along  the  constant  heat  curve 
Y,  the  whole  of  the  heat  available  at  N  would  exist  in  the  steam 
after  falling  to  Z,  and  would  be  rejected  along  the  line  ZF. 
The  heat  so  rejected  would  be 

H2'  =  eLTea,GFZJG, 

which  equals  Hi,  the  original  heat  in  the  steam  at  N.  The 
total  amount  of  heat  available  at  A^  would  thus  fall  in  tempera- 


VELOCITY  AND  FRICTIONAL  RESISTANCES,  81 

ture  without  doing  any  work  towards  increasing  its  own  velocity 
— that  is,  the  velocity  at  Z  being  Vo', 

TV=  164.4x778(i7i-i/2')l^  =  0, 

since  Hi  =H2. 

The  work  of  friction  is  represented  by  the  area  ANZA. 
It  is  obxdous  that  the  work  of  friction  causes  the  entropy  of  the 
steam  at  its  lowest  temperature  to  be  greater  than  it  wouid  be 
if  adiabatic  expansion  occurred  from  N  to  A.  The  heat  re- 
jected is  therefore  made  greater  by  an  amount  represented  by 
the  area  ADJZA,  which  represents  the  actual  loss  of  kinetic 
energy  due  to  friction.  The  work  of  friction  represented  b}- 
area  ANZ  is  all  returned  to  the  steam,  and  serves  to  increase 
its  dryness  fraction,  but  in  doing  so  it  decreases  the  amount  of 
energy  the  steam  is  capable  of  gi^'ing  up  towards  increasing 
its  own  velocity. 

Exam'ple. 

Let  the  initial  pressure  at  iV  =  loO.O  pds.  sq.  in.  =  7)l; 
''     ''    final  "        "    Z=     1.5    "     ''   "  =7^2; 
"     ''    quality  of  steam  at  iV=     0.90; 
"     "    steam   fall   in    pressure   along   the   constant   heat 
curve  Y. 

Heat  of  liquid  at  150  pds.  abs.=330  B.T.U. 

"    ''  vaporization  at  150  pds.  abs.  =  861  B.T.U. 
0.90x861+330  =  1105  B.T.U.  total  heat  per  pd.  at  N. 

Since  the  heat  at  Z  is  to  be  also  1105  B.T.U.  and  the 
total  heat  of  saturated  steam  at  L  is  1117  B.T.U.,  the  quality 
at  Z  may  be  found  as  follows: 

Heat  of  liquid  at  F  =  S4.1  B.T.U. 

Quality  at  Z  =  (1105-84.1)-(1117-84.1) 


entropv  FZ        

-     ,    '•    ^.  =0.987. 
entropy  FL 


82  STEAM-TURBINES. 

Entropy  of  vaporization  at  1.5  pds.  pres.  =  1.790  =  en- 
tropy FL. 

Entropy  FZ  =  1.79  X  0.987  =  1 .766. 

Heat  beneath Fiy  =  330-   84=   246  B.T.U.  1   =Hi=heatm 

"  "      HN=  0.9X861=  775      "        I      steam   at 

"         I      initial    con- 

1021      ' '  ditions. 

Heat  beneath  i^Z  =  entropy  FZxahs.  temp,  of  steam  at  1.5 
pds.  pres. 
=  1.77x577  =  1021  B.T.U. 
=  heat  in  steam  at  final  condition  at  Z 

=  H2'. 

It  is  evident  that  Hi—H2'  =  0  and  therefore  that  no 
velocity  would  result  from  fall  of  temperature  along  the 
curve  Y.  It  is  to  be  noticed  that  in  the  above  example  the 
heat  represented  by  area  ADJZA  equals  that  by  FHNAF, 
since  GFHNDG  equals  GJZFG,  and  GDAFG  is  common  to 
both  areas.  Thus  the  initial  available  heat  just  equals  the 
loss  of  heat  caused  by  the  steam  following  the  curve  of  con- 
stant heat. 

In  general  the  steam  in  a  nozzle  expands  according  to 
some  such  curve  as  NX  between  NA  and  NZ,  and  the  shaded 
area  NAXN  represents  the  friction  work,  while  AXKDA  rep- 
resents the  loss  of  energy  due  to  the  resistance.  Since  the 
friction  work  is  all  returned  to  the  steam  as  heat  it  is  not  nec- 
essary to  determine  its  value,  but  the  Joss  of  energy  due  to  the 
frictional  resistance  is  one  of  the  most  important  items  con- 
nected with  steam-turbine  calculations. 

Let  Hi  =heat  in  entering  steam,  as  defined  on  p.  80; 

7^2  =  heat  rejected  after  adiabatic  expansion  to  the  lower 

pressure  p2', 
//^  =  heat  of  vaporization  of  dry  saturated    steam   at 
pressure  p2- 
If  the  steam  falls  in  pressure  adiabatically,  and  without 


VELOCITY  AND  FRICTIOXAL  RESISTAXCES.  S3 

frictional  resistance,  the  heat  given  up  is  H1-H2  and  the 
velocity  developed  by  the  steam-jet  is 

F=  164.4  X  778  X(i/i-i/2)}*. 

If  y  one-hiindredths  of  the  heat  H^  -Ho  is  lost,  due  to  the  fric- 
tional resistance  corresponding  to  fall  down  the  curve  A^A^, 
Fig.  28,  the  heat  given  up  will  be  {l-ij)(Hi-H2)  and  the 
resulting  velocity  will  be 

F=|64.4x778x(l-?/)(^i-i72)l^  .    .    .     (17) 

The  quality  of  the  steam  after  expanding  to  7)2  against 
the  resistance  will  be  higher  than  after  adial^atic  expansion 
b}'  an  amount  repre.sented  by  AX-^FL,  Fig.  26.  This  ratio  is 
the  same  as  the  ratio  between  the  quantities  of  heat  beneath 
AX  and  FL  respectively.  But  the  loss  of  heat,  y{Hi—H2^, 
is  equal  to  the  heat  represented  by  the  area  beneath  AX,  and 
the  heat  beneath  FL  is  equal  to  the  heat  of  vaporization. 
H ^,,  of  steam  at  po.  Therefore  the  increase  of  quality  of  the 
steam,  due  to  the  resistance,  is 

x"  =  y{H,-Ho)-^H^ (18) 

The  quality  at  .Y,  Fig.  26,  is  the  sum  of  the  per  cent  of  steam 
at  A  and  the  percentage  represented  by  the  above  expression. 
Knowing  the  weight  of  steam  flowing  through  a  passage  per 
unit  of  time,  the  volume  may  be  determined  from  the  quaUty 
of  the  steam.  Knowing  the  volume  and  the  velocity  the 
proper  cross-sectional  area  for  the  passage  may  be  determined. 

Example. 

Let  the  initial  pressure  be  150.0  pds.  per  sq.  in.  abs.  =pi; 
"     ''    final  "         "       1.5    "      ''     "    "     "    =p2', 

"     "    loss  of  energy  in  the  passage  be  15%  or  ?/=0.15; 
**"     "    initial  quaUty  of  steam  be  0.98. 


84  STEAM-TURBINES. 

Then  i7i  =1090  B.T.U.  =heat  above  point  i^,  Fig.  26. 
Entropy  at  N  (Fig.  26)  =  1.543. 

Entropy  i^A  =  1.543  -entropy  5(7=  1.543  -0.157  =  1.386. 
/^2  =  entropy  FAXah^.  temp,  corresponding  to  p2  =  1.386 
X  577  =  800  B.T.U. 

Velocity  7=  {64.4x778x0.85(1090-800)  \  *  =  3500  ft.  per  sec. 
The  quality  of  steam  at  A  would  be 

x'  =  Entropy  FA  ^  entropy  FL  =  1.386  ^  1.791 =0.774,  approx. 

This  quality  is  increased  by  the  amount 

x"  =  ?/(Fi-i72)^/f,  =  0.15X290 -1033  =0.042, 

or  the  quality  at  X  is  x'  +  x"  =  0.774 +  0.042  =0.816. 

The  specific  volume  of  steam  at  p2,  or  1.5  pds.  abs.,  is  227 
cu.  ft.  Neglecting  the  volume  of  the  water  of  condensation, 
the  volume  per  pound  of  the  steam  in  the  present  example  is 

227X0.816  =  185  cu.  ft. 

In  any  conduit  or  passage,  if  a  steady  flow  of  fluid  takes 
place,  the  volume  flowing  per  second  is 

Q=AV, 

where  A  is  the  area  of  cross-section  of  the  passage  and  V  is 
the  velocity.  If  Q  is  in  cu.  ft.,  then  A  should  be  in  square  ft. 
and  V  in  ft.  per  second.  If  the  passage  varies  in  cross-section 
to  Ai  and  the  quantity  Q  remains  the  same,  then  Q=AiVi. 
In  general,  for  steady  flow  the  equation  may  be  written 

Q=AV=AiVi=A2V2,etc. 

If  the  volume  varies,  then  for  a  given  area  of  cross-section 
the  velocity  will  vary.  In  the  present  example,  suppose 
0.25  pd.  steam  flows  through  an  expanding  nozzle  and  reaches 
at  the  large  end  a  velocity  of  3500  ft.  per  second,  as  found 
above,  corresponding  to  a  pressure  of  1.5  pds.  abs.  per  sq.  in. 

The  volume  per  pd.  has  been  found  to  be  185  cu.  ft.,  or 


VELOCITY  AND   FRICTIOXAL  IlESISTANCES. 


S5 


the  vol.  flowing  per  second  is  0.25x185=40.2  cu.  ft.  It  is 
required  to  find  the  cross-sectional  area  of  the  nozzle  at  the 
large  end. 

Q  =  46.2  cu.  ft.  per  sec. 

F  =  3500  ft.  per  sec. 

^4  =Q- 7  =  46.2^-3500  =0.0132  sq.  ft. 
or  0.0132  X 144  =  1.9  sq.  inches. 

Problem. — Find  the  smallest  cross-section  of  a  conically 
divergent  nozzle  for  carrying  out  the  expansion  indicated 
in  the  above  problem,  and  find  three  intermediate  cross-sec- 
tions, where  the  pressures  will  be  75,  50,  and  25  pds.  abs.  respect- 
ively. ]\Iake  the  nozzle  8  inches  long  and  sketch  it  on  cross- 
section  paper. 

CALCULATIONS. 


Calculations  for  P2=  1-5 
Pounds  Absolute. 


(0.98X861) +  (330 -84)  = 
(B.T.U.) 


En. 

Ebg 

Efa=En-Ebg 

i/2  =  abs.  temp.  TzXEfa 

(B.T.U.) 

H,-H2 (B.T.U.) 

F  =  V[64.4X778X(1.00-0.15) 

(H.-Hi)] (ft.  per  sec.) 

Efl  =  entropy    of    vaporization 

at  po 

Quality  at  A  =  EpA  -^  EpL  = 

1.386 


1.791 
Heat  of  vaporization  at  po  =  Hv 

(B.T.U.) 
Increase    in   quality    along   AX 

=  y{H,-H,)-^Hv 

Quality  at  X  =  0.774  +  0.042 

Sp.  vol.  dry  steam  at  p2  (cu.  ft.) .  . 
Vol.    per     pd.     of     wet    steam, 

227X0.816  =  1-2 

Vol.  per  sec.  =  0.25  X 185  =  Q 

Area  (sq.   in.),  cross-section  of 

46.2X144 
nozzle  =  Q.T  =-3^^  .... 

Diameter  of  nozzle,  ins 


P2=1.5 

Pds. 
Abs. 


1090 
1.543 
0.157 
1.386 

800 
290 

3500 

1.791 

0.774 

1033 

0.042 

0.816 
227 

185 
46.2 

1.9 
1.56 


P2  =  7.5 
Pds. 
Abs. 


1025 
1.543 
0.264 
1.279 

820 
205 

2960 

1.542 

0.829 

988 

0.0311 
0 .  860 
50.0 

43.0 
10.75 

0.523 

0.819 


P2=15 
Pds. 
Abs. 


992 
1,543 
0.314 
1.229 

829 
163 

2640 

1.432 

0.856 

965 

0.0253 
0.881 
26.1 

23.0 
5.75 

0.313 
0.631 


P2  =  25 
Pds. 
Abs. 


965 
1 .  543 
0.354 
1.199 

840 
125 

2310 

1.350 

0.888 

946 

0.019S 
0 .  908 
16.1 

14.6 
3.65 

0.227 
0.538 


P2  =  50 
Pds. 

Abs. 


924 
1.543 
0.411 
1.132 

840 
84 

1890 

1.237 

0.915 

917 

0.0137 
0.927 
8.41 

7.81 
1.95 

0.14S 
0.434 


P2=/0 

Pds. 
Abs. 


897 
1.543 
0.446 
1.097 

842 
55 

1530 

1.169 

0.939 

898 

0.0092 
0.948 
5.75 

5.28 
1.32 

0.124 
0  398 


86  STEAM-TURBINES. 

The  curves  on  Plates  IV,  V,  and  VI  show  that  less  steam 
flowed  through  the  divergent  nozzles  at  the  right  than  through 
the  orifices  at  the  left.  Also  in  the  case  of  the  nozzle  with 
rounded  entrance  the  maximum  rate  of  flow  was  reached  by 
the  time  the  ratio  of  back  pressure  to  initial  pressure  reached 
the  value  0.85.  It  seems  from  the  curves  on  Figs.  52  to  56, 
and  from  data  regarding  orifices,  that  the  pressure  in  general 
falls  at  the  throat  of  the  nozzle  and  then  rises  again.  Ex- 
periments indicate  that  the  pressure  in  the  throat  of  the  nozzle 
falls  to  that  value  which  gives  the  maximum  flow  of  steam 
by  weight  at  any  given  initial  pressure.  By  calculating  the 
energy  given  up  during  the  fall  in  pressure,  the  corresponding 
velocity  may  be  ascertained,  and  the  proper  cross-sectional 
area  for  the  smallest  part  of  the  nozzle  may  be  found. 

Referring  to  Fig.  26,  to  calculate  the  proper  diameter  of 
nozzle  for  the  present  example,  where  pres.  =  112  pds.  abs., 

The  entropy  FL  =  1.10, 
FA  =  1.0Q. 

Therefore  the  quality  at  A  =0.96  or  4%  of  the  steam  is  con- 
densed in  passing  the  throat  of  the  nozzle. 

/fi  =  844  +  24  =868  B.T.U. 

H2  =  EpA  X  7^2  =  1.06  X  797  =  845       " 

H1-H2  =23       '' 

Neglecting  the  loss  that  may  have  occurred  up  to  the  point 
under  consideration, 


Velocity  in  throat  =V778x64.4x23  =  1070  ft.  per  sec; 

Specific  volume  at  112  pds.  =3.96  cu.  ft. 

Volume  at  quality  0.96  =  3.8  cu.  ft. 

Volume  passing  per  second  =  0.25x3.8 =0.95  cu.  ft. 


VELOCITY  AND  FRICTIONAL  RESISTANCES.  87 

0.95x144 
Area  of  cross-section  =   '  ,„_„ —  =  0.128  sq.  in. 

10/0 

Diameter  required  =0.404  inch  or  approximately  13/32". 

Having  found  the  largest  and  smallest  diameters  of  the 
nozzle  the  latter  may  be  drawn  to  scale.  The  length  must 
be  decided  upon  according  to  circumstances  and  the  designer's 
judgment  as  to  the  effect  of  length  and  angle  of  divergence 
upon  the  friction  losses.  The  points  in  the  length  of  the  nozzle 
where  the  previously  calculated  pressures  ^^ill  occur  may  be 
located  with  the  assistance  of  a  pair  of  dividers  for  finding 
the  diameters  corresponding  to  the  areas  for  their  respective 
pressures. 

Another  form  in  which  the  problem  may  present  itself  is, 
given  the  initial  and  final  conditions  of  the  steam,  to  find  what 
loss  of  energy  will  occur  by  reason  of  resistance  in  a  given 
nozzle. 

Let  it  be  found  from  a  test  that  at  the  end  of  expansion 
from  150  lbs.  abs.  to  H  lbs.  abs.  the  quality  of  exhaust  is  0.816. 
It  is  required  to  find  the  percentage  of  loss  due  to  frictional 
resistance  in  the  nozzle. 

.\s  before,   /fi  =  1090  B.T.U.     /^2  =  800  B.T.U. 

Quality  at  A  =  quality  due  to  adiabatic  expansion =0.774. 
Increase  in  quality  represented  by  .4  A'  =  0.816  —0.774  =  0.042. 
Hence,  y(Hi-H2)^H  ^=0:2Sly  =  0m2. 

0  042 
y = loss  of  energy  =  ^~^  =  0.15,     or     15%. 

This  prol:»lem  being  the  inverse  of  the  one  pre\'iously  worked 
out,  the  result  just  found  is  the  same  as  the  assumption  of 
energy  loss  in  the  previous  example. 

The  method  developed  in  Chapter  IV  for  simphfying  com- 
putations of  velocity  by  means  of  the  heat  diagram  may  be 


88  STEAM-TURBINES. 

used  equall}^  well  in  cases  involving  the  allowance  for  losses. 
Thus,  instead  of  equation  (17), 

may  be  written 

F  =  158K^l+^2)(^l-7^2)(l-^)}^      .     .     (19) 

where  Ex  and  E2  represent  entropy  changes  at  absolute  tem- 
peratures Ti  and  T2  respectively,  as  before. 

If  the  values  of  y  are  known  for  a  given  type  of  nozzle 
operating  under  given  pressures,  the  velocities  may  be  pre- 
dicted. It  is  necessary  first,  however,  to  analyze  results  ob- 
tained by  experiment  in  order  to  find  proper  values  for  the 
coefficient  y. 

Suppose,  for  example,  that  curves  representing  actually 
obtained  results  from  a  given  type  of  orifice  or  nozzle  have 
been  plotted.  Curves  A  on  Plates  II  and  III  are  of  this  charac- 
ter. Curves  B  are  plotted  from  equation  (17),  using  the  value 
y^O.  The  loss  of  velocity  in  the  actual  orifice  or  nozzle  is 
then  represented  by  the  distance  between  the  curves  A  and  B. 
Let  it  be  required  to  find  the  friction  loss  y  at  different  initial 
pressures,  and  to  use  these  values  for  obtaining  a  curve  coin- 
ciding with  curve  A. 

Let  the  velocity  from  the  actual  curve  A  be  called  Va, 
"     ''         ''    ^      "      "   ideal       "     B  "      "      Fj,. 

Then  Fa=\/50103(//i -//2)(l-2/); 

y6=\/50103(//i-//2) ; 

V  /V  \2 

Y^=Vl-y    or    y  =  l-[Yj- 

Values  of  y  maj^  be  plotted,  as  is  done  at  the  bottom  of 
Plates  II  and  III,  from  calculations  given  at  top  of  page  89. 
These  calculations  apply  to  the  curves  A  and  C,  Plate  III. 
The  curves  show  that  as  the  initial  pressure  is  decreased 


VELOCITY  AND  FRICTIONAL  RESISTANCES. 


89 


Initia  Pressure 

Vc 

-'-(f:)'- 

Absolute. 

Va- 

Vb. 

Vb' 

60 

1830 

2260 

0,81 

0,44 

100 

2370 

2640 

0.90 

0.19 

140 

2680 

2870 

0.94 

0  12 

180 

2890 

3030 

0,95 

0,09 

220 

3050 

3140 

0.97 

0.06 

the  friction  loss  in  the  expanding  nozzle  increases,  this  being 
especially  true  for  pressures  below  100  pounds  per  square  inch. 
In  the  case  of  the  orifice  in  a  thin  plate,  on  the  contrary,  the 
losses  are  less  at  low  pressures  than  at  high  pressures.  The 
curve  of  losses  on  Plate  II  shows  the  value  of  y  to  increase 
slightly  with  the  pressure,  but  the  change  indicated  is  so  small 
that  the  value  of  y  for  this  orifice  may  be  regarded  as  constant 
at  about  0.26.  The  values  for  the  orifice  and  for  the  expand- 
ing nozzle  are  equal  at  about  80  pounds  absolute  initial  pressure. 
For  the  nozzles  experimented  with  by  Messrs.  Jones  and 
Rathbone  the  losses  at  100  pounds  and  50  pounds  initial  pressure 
absolute  were  as  shown  in  the  following  table.  The  back  pressure 
was  atmospheric  in  all  cases.  In  all  the  straight-bore  nozzles 
the  losses  are  higher  for  100  pounds  initial  pressure  than  for 
50  pounds,  but  in  the  case  of  the  expanding  nozzle  the  reverse 
is  true,  the  value  of  y  at  100  pounds  being  only  40  per  cent 
of  that  at  50  pounds. 


Diameter 

Initial 

Loss  Due  to  Friction. 

Kind  of  Nozzle. 

Pressure, 
Pounds 

Absolute. 

Per  Cent  of 
Ideal. 

Value  of  y. 

^ 

Straight  bore,  sharp  entrance 

100 

11.3 

0.222 

A 

'           '            * ' 

50 

7.6 

0.163 

i 

100 

13.2 

0  255 

i 

1 1           1 

(         It            11 

50 

10.5 

0,208 

1 

4 

1 1           I 

'  rounded      " 

100 

10.6 

0.226 

i 

1  {           1 

(         <  (            /  i 

50 

8.6 

0.164 

i 

Expand.    ' 

I         ( (            ( ( 

100 

5.7 

0.125 

1 
4 

50 

16,7 

0.312 

t 

Straight     ' 

'      sharp        ' ' 

100 

7,5 

0.145 

f 

50 

3.6 

0.077 

90 


STEAM-TURBINES. 


PLATE  II. 


3100 
3000 
2900 
2800 
2700 
2G00 
2500 
3400 
2300 
2200 
2100 
2000 
1900 

^^ 

/B 

y 

/^ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

^A 

/ 

^ 

} 

/ 

/ 

/ 

I 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

// 

/ 

/ 

/ 

iroo 

/ 

1 

C 



1600 

1400 

■ 

40 
30 

20  o 

3 

.10  S 


40 


80         100        120        140        160        180        200 
Initial  Pres.  -  Pds.  per  sq.  in.  Absolute 


220 


240 


2uO 


Curve  A,  Mr.  Rosenhain's  experiments;  velocity  corresponding  to  meas- 
ured reaction  of  the  jet  from  an  orifice  in  a  thin  plate, 

Cui've  B,  calculated  velocity,  upon  the  assumption  that  all  the  heat 
energy  concerned  in  the  drop  from  the  higher  pressures  before  the  orifice 
to  the  constant  atmospheric  pressure  beyond  the  orifice  was  converted 
into  the  kinetic  energy  of  the  jet  of  steam. 

Curve  C,  values  of  y  at  different  pressures. 


VELOCITY  AND   FRICTIONAL  RESISTANCES.  91 

PLATE  m. 


so         100        120        140        IGO        ISO 

Initial  Abs.  I'lfssure  Pounds  pei'Sii.  In. 

Curve -4,  Mr.  Rosenhain's experiments;  velocity  correspondinsrto  measured 
reaction  of  the  jet  from  an  expanding  nozzle.     (Nozzle  Xo.  Ill  A,  p.  108.) 

Curve  B.  calculated  velocity,  assuming  that  all  the  heat  energy  con- 
cerned in  the  drop  from  the  higher  pressures  b-efore  the  nozzle  to  the  con- 
stant atmospheric  pressure  beyond  was  converted  into  the  kinetic  energy 
of  the  jet  of  steam. 


92 


STEAM-TURBINES. 


Calculatioxs  for  Curves  A  and  B  on  Plate  III. 

Least  diameter  of  nozzle.  ...   0 .  1882"      Length  of  nozzle 0 .  79" 

Greatest  diameter  of  nozzle .   0 .  2550"      Least  area  of  cross-section .   0 .  2782" 


Initial 
Pressure, 

Pounds 
Absolute. 

Ti 

^3 

Ti-Ts 

Ei  +  E, 

Pounds 
Diseharg'd 
per  Second 

as 
Measured. 

Reaction 
Pounds, 
Observed. 

Velocity 

from 
Reaction. 

Velocity 
Ideal. 

35 

720 

673 

47 

2.67 

0.013 

0.45 

1120 

1770 

55 

748 

673 

75 

2.55 

0.021 

1.10 

1690 

2180 

75 

768 

673 

95 

2.48 

0.028 

1.80 

2070 

2420 

95 

785 

673 

112 

2.42 

0.038 

2.70 

2290 

2600 

115 

799 

673 

126 

2.37 

0.044 

3.45 

2520 

2730 

135 

811 

673 

138 

2.34 

0  052 

4.25 

2640 

2840 

155 

822 

673 

149 

2.31 

0.059 

5.05 

2760 

2930 

175 

831 

673 

158 

2.28 

0  066 

5.85 

2860 

3000 

195 

840 

673 

167 

2.25 

0.073 

6.65 

2940 

3060 

215 

849 

673 

176 

2.23 

0.079 

7.45 

3040 

3130 

CHAPTER  VI. 

EXPERIMENTAL  WORK  OX  FLOW  OF  STEAM    THROUGH 
ORIFICES,  NOZZLES,  AND  TURBINE-BUCKETS. 

In  the  design  of  nozzles  and  steam-channels  in  general  the 
following  questions  are  involved: 

{a)  The  weight  of  steam  that  will  flow  through  when  cer- 
tain pressures  exist  at  the  inlet  and  outlet  ends  respectively. 

(b)  The  velocity  attained  by  the  issuing  jet  of  steam  when 
a  known  weight  per  second  is  flowing. 

(c)  The  heat  expenditure  necessary  in  order  to  produce  a 
given  amount  of  kinetic  energy  in  the  jet  as  it  leaves  the  nozzle 
or  passageway. 

Experiments  to  determine  the  above  have  been  made  in 
various  ways,  and  among  the  methods  used  are  the  following: 

1.  Steam  caused  to  flow  from  a  higher  to  a  lower  pressure 
through  various  shapes  of  orifice  and  nozz!e,  and  the  steam 
condensed  and  weighed.  The  results  obtained  by  this  method 
give  the  weight  of  steam  that  the  orifices  and  nozzles  will  dis- 
charge per  unit  of  time  under  differing  inflow  and  outflow 
pressures  This  information,  however,  does  not  give  the  data 
for  calculating  the  velocity  attained  by  the  steam,  because 
the  specific  volume  of  the  steam  at  different  points  along  the 
nozzle  depends  u]3on  the  pressures  at  those  points,  and  the 
latter  are  not  known.  Further,  the  nozzle  allowing  the  greatest 
weight  of  steam  to  pass  is  not  necessarily  that  giving  the  greatest 
velocity  of  outflow  or  the  greatest  energy  of  the  jet. 

93 


94  STEAM-TURBIXES. 

2.  Steam  flowing  as  described  in  1,  but  pressuies  along  the 
nozzle  investigated  by  means  of  a  small  ''searching-tube" 
held  axially  in  the  nozzle.  The  tube  has  a  small  hole  in  its 
wall,  and  by  moving  the  tube  along  the  nozzle  bore  the  hole 
occupies  various  positions  and  indicates  on  a  gage  connected 
to  the  end  of  the  tube  a  more  or  less  close  approximation  to 
the  pressures  existing  at  the  points  where  the  hole  is  brought 
to  rest.  It  makes  a  considerable  difference  in  the  results, 
however,  whether  the  hole  in  the  tube  is  perpendicular  to  the 
axis  of  the  tube  or  slants  in  the  same  direction  as  the  flow  of 
steam  or  in  the  opposite  direction.  Holes  have  also  been 
drilled  in  the  nozzle  walls  and  pressures  measured  at  those 
points.  From  such  observations  of  pressures,  the  specific 
s^olume  of  the  steam  at  various  cross-sections  has  been  cal- 
culated, and,  the  rate  of  steam-flow  being  known,  the  velocity 
at  the  different  sections  has  been  approximately  found.  Tliis 
method  is  open  to  the  objections  that  the  accuracy  of  the  pres- 
sure readings  is  very  questionable,  and  the  extent  to  which  the 
steam  fills  out  the  cross-sectional  areas  of  the  nozzles  is  not 
known.  However,  mu  h  very  valuable  information  has  been 
obtained  by  this  means  as  to  the  variation  of  pressure  and  the 
vibrations  of  the  steam  in  the  nozzle,  the  effect  of  varying 
back  pres  ures,  etc. 

In  experiments  made  in  Sibley  College  during  1904-5  by 
Messrs.  Weber  and  Law,  the  searching-tube  was  arranged  so 
it  communicated  the  pressure  in  the  nozzle  to  the  piston  of  a 
s:eam-engine  indicator,  and  thus  an  autographic  representa- 
tion of  the  pressure  changes  was  obtained.  These  experiments, 
and  others  along  the  same  line,  will  be  referred  to  later. 

3.  B}'  arranging  the  nozzle  so  that  as  the  steam  flows  out 
of  it  the  reaction  against  the  nozzle  accompanying  the  accelera- 
tion of  the  steam  can  be  measured,  it  is  possible  to  ascertain 
the  veloc'ty  the  steam  attains.  The  rate  of  steam-flow  is 
measured  by  condensing  and  weighing,  and  the  velocity  in 
feet  per  second  equals  the  reaction  in  pounds  multiplied  l^y 
g  (-32.2)   and  divided  by  the  weight  of  steam  flowing  per 


EXPERIMENTAL  WORK  OX  FLOW  OF   STEAM.  95 

second.  By  measuring  the  weight  and  inlet  and  outlet  tem- 
peiatures  of  the  condensing  water,  as  well  as  the  weight  of 
condensed  steam  the  heat  given  up  in  the  nozzle  can  he  found 
and  the  prime  object  of  such  experiments  may  be  attained; 
that  is,  the  efficiency  of  the  nozzle  may  be  found — or  the  amount 
of  kinetic  energy  in  foot-pounds  that  can  be  produced  by  one 
heat-unit  in  the  entering  steam. 

4.  If  a  nozzle  delivering  W  pounds  of  steam  per  second 
discharges  into  buckets  having  known  entrance  and  (>xit 
angles,  the  velocity  of  the  jet  may  be  computed  by  n:cans  of 
formula  G  on  page  12.     See  also  plate  facing  page  128. 

Weight  of  Steam  Flowing  Through  Orifices  axd  Nozzles 
AS  Found  Experimentally  by  Professor  Gutermuth. 

Curves  1,  2,  3,  and  4,  on  Plates  IV,  V,  and  VI,  show  the 
weight  of  steam  which  flowed  from  the  four  orifices  shown 

for  varjdng  values  of  -^  and  for  varying  initial  pressures.     In 

each  case  more  steam  flowed  through  the  orifice  mth  the 
rounded  entrance  than  through  that  wdth  the  sharp- edged 
entrance,  and  in  each  case  the  weight  of  steam  flowing  per 
second  reached  a  maximum  value,  beyond  which  the  weight 
per  second  did  not  increase  or  decrease  as  the  pressure  p2 
was  decreased.  The  question  of  the  flow  of  steam,  by  weight, 
depends  upon  the  pressures  immediately  in  the  orifice,  as 
well  as  upon  those  in  the  inflow  and  outflow  vessels.  Curves  5, 
which  represent  the  adiabatic  flow  of  a  gas  which  has  the 
same  ratio  of  specific  heats  as  dry  and  saturated  steam,  accord- 
ing to  the  equation  developed  in  Chapter  II,  are  not  applicable 
to  the  case  of  steam-flow,  unless  the  steam  remains  dry  and 
saturated  during  expansion,  or  else  is  initially  superheated  and 
remains  superheated  during  expansion.  Steam  in  expanding 
adia'atically  from  a  saturated  condition  becomes  partially 
condensed, — the  specific  heat  of  the  mixture  changes  and 
the  Tow  is  not  like  to  that  of  a  gas.  If  the  steam  remained 
sup':rheated,    or    dry    and    saturated,    during    expansion,    the 


96 


STEAM-TURBINES. 


'oas  jad  paSj'eqostp  spunoj 


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EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM. 


97 


Pounds  discharged  per  sec. 


Pounds  discharged  per  sec. 


98 


S  TEA  M-  T  UR  BINES. 


•03S  J9d  paSjuqosip  spunoj 


•oas  aad  paSj^qosip  spuno<j 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM.  99 

formula  for  the  flow  of  gas  would  apply  to  that  of  the  steam. 
As  it  is,  however,  the  point  at  which  the  maximum  flow  of 
steam  will  occur,  through  an  orifice  having  well-rounded  entrance, 
agrees  more  or  less  closely  with  the  indications  of  the  equation 
for  a  gas,  as  is  seen  by  the  curves  given,  and  with  certain  modi- 
fications the  equation  may  be  used  to  indicate  the  conditions 
of  maximum  flow.  A  very  useful  equation  was  developed 
by  j\Ir.  R.  D.  Napier,  and  modified  by  Professor  Rankine, 
based  upon  experiments  by  Napier  and  the  equation  under 
discussion.  The  discharge  through  an  orifice  a  sq.  ins.  area 
from  a  pressure  pi  on  one  side  to  a  lower  pressure  7)2  on  the 
other  side  may  be  calculated  as  follows,  according  to  Napier's 
formula: 

W  =  ^    if    —  =  or  is  less  than  0.60. 
/O  pi 


When  ^  is  greater  than  0.60,  W  =^-|\|  j  ^^^luM  \ . 
Pi  '         42\  [       2p2      J 

Thus,  in  the  case  of  curve  2,  Plate  IV,  the  discharge  accord- 
ing to  this  expression  w^ould  be 

„,    0.0355X132    ^^^_ 

H  = ^ =0.0669  pound  per  second. 

The  observed  maximum  flow  is  0.063  + pounds,  or  about  94% 
of  that  given  by  the  equation. 
Similarly,  on  Plate  V,  curve  2, 

The  observed  maximum  flow  is  0.05,  or  about  95%  of  that  given 
by  the  equation. 

On  Plate  VI,  curve  2, 

„.     0.0355X103    ^^,^„ 

TI  = ^7^ =0.0523  pound. 


100  STEAM-TURBINES. 

The  observed  maximum  flow  is  0.050,  or  about  95.5%  of  that 
given  by  the  equation. 

The  above  equation  may  be  taken  as  a  guide  for  calcu- 
lating the  maximum  flow  of  steam  when  the  ratio  p2-^Vi  is 
not  greater  than  about  0.6,  but  it  evidently  does  not  apply 
closely  unless  the  orifice  has  a  well-rounded  entrance. 

It  is  to  be  observed  that  curves  4  on  Plates  IV  and  VI,  for 
the  divergent  nozzles,  show  a  smaller  steam  weight  discharged 
per  second  than  is  discharged  from  the  plain  orifice  2.  This, 
however,  does  not  mean  that  the  velocity  in  the  divergent 
nozzle  is  less   than  that  in  the  plain  orifice. 

The  table  opposite  shows  the  results  of  experiments  with 
the  orifices  on  Plate  VII,  together  with  the  calculations 
of  the  steam- flow  by  Napier's  formula  and  by  the  thermo- 
dynamic formula  which  was  developed  in  Chapter  IV.  All 
the  experiments  excepting  those  by  Professor  Peabody  were 
made  in  the  Sibley  College  laboratories  under  the  direction 
of  Professor  R.  C.  Carpenter. 

It  has  been  shown  in  the  preceding  discussion  that,  at  least 
for  small  diameters  of  opening,  it  is  possible  to  calculate  very 
closely  the  maximum  weight  of  steam  discharged  per  unit 
of  time  under  given  initial  and  final  pressures.  It  has  been 
quite  thoroughly  demonstrated  that  after  a  certain  diminution 
of  back  pressure,  the  rate  of  flow,  by  weight,  ceases  to  increase, 
and  that  it  remains  sensibly  constant  during  further  reduction 
of  back  pressure.  The  tables  on  page  109,  calculated  from 
the  experiments  of  Mr.  Walter  Rosenhain,  and  of  Mr.  George 
Wilson,  further  confirm  these  statements. 

The  question  as  to  the  rate  of  increase  of  flow  up  to  the 
maximum  rate  has  been  answered  for  convergent  nozzles  of 
certain  sizes  by  the  formula  by  Mr.  R.  D.  Napier  (see  page  99), 
the  work  of  Professor  Rateau  (see  page  106),  and  that  of  Pro- 
fessor Gutermuth  (see  Plates  IV,  V,  and  VI). 

The  rate  of  flow,  by  weight,  up  to  the  point  of  maximum 
flow,  depends  very  largely  upon  the  shape  of  the  inlet  end 
of  the  orifice  or  nozzle, — whether  the  inlet  is  rounded  or  has 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


101 


FLOW   OF  STEAM  THROUGH   ORIFICES. 


Pressure  above 
Atmosphere  per 

Ratio  of 
Absolute 

Flow  in  Pr 
per  Hot 

unds 

Apparent 
Coefficient 

Sq 

uare  Inch. 

C  u 
3  C 
C'-i 

is 

Pressures. 

•0 

of  Flow. 

6 

C 

0 
0 
« 

0 

4J 

C 

5.^  u 

C      iH      ^ 

8.S6 

si 

a 
W 

2W 

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hi 

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li 

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m 

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pq 

m 

1 

2 

3 

4 

5 

6 

7 

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9 

10 

11 

12 

13 

Orifi 

ce  (a 

i).    P 

erry's 

Expe 

riment 

s. 

I 

II4-7 

66.4 

-II. 7 

14.4 

.021 

.624 

140 . 2 

96  .45 

3 '.1-9 

320.2 

326 

1.045 

1 .020 

2 

112. 8 

64.9 

+  14 

7 

14 

4 

.228 

.623 

245-6 

96.56 

36). S 

317.3 

321.2 

1. 1 30 

1 .  120 

3 

io8 

61.3 

52 

7 

14 

4 

.548 

.618 

298.4 

97.6 

321  .7 

307.9 

308.3 

1.045 

1.047 

4 

I  lO.  1 

66.2 

72 

3 

14 

4 

.696 

.650 

312. 1 

96.61 

348.8 

308.2 

314-4 

1. 131 

I .  no 

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89.1 

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0 

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.841 

326.9 

96 

267.1 

247.8 

311. 6 

1.077I    .857 

6 

no. 5 

103-7 

106 

9 

14 

4 

.971 

.948 

334.8 

98.46 

144.2 

151. 8 

3154 

.956 

.456 

7 

74-4 

68.6 

71 

9 

14 

4 

■  971 

•  940 

311. 3 

99-4 

107 

118. 9 

224.  2 

.899 

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8 

5°. 4 

40. 6 

42 

14.4 

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•  542 

285.9 

99.6 

107 

141 . 1 

163.6 

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.776 

Or 

ifice 

(a„). 

I 

III  .9 

59-2 

—  10.9 

14.39 

■  037 

.583 

148.6 

97-26 

330.9 

315.9 

318.9 

1.047 

1 .037 

2 

114. 8 

61.2 

14.8 

14 

39 

.226 

.585 

248.4 

96.7 

336. 5 

319.7 

326. s 

1.052 

1.03 

,? 

99-3 

57-2 

52.4 

14 

43 

.587 

.634 

295.7 

96.9 

289.1 

283.8 

287.2 

1 .02 

1 .0006 

4 

112. s 

70 

72.3 

14 

43 

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.668 

312.4 

96.6 

3i3-8|274-2 

320.4 

1.136 

.987 

5 

IIS. 5 

93.3 

93.2 

14 

43 

.828 

.830 

326.9 

96.4 

262       263.1 

328.1 

•  994 

•  798 

6 

II  2  .6 

109.  2 

108.8 

14 

43 

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.978 

336.5 

98.5 

38.9  114. 2 

320.8 

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.121 

7 

94-7 

50.5 

14.8 

14 

43 

.  267 

■  591 

247.1 

96.6 

286.3  271 .4 

275-6 

1.054 

1.037 

8 

74-7 

39.4 

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14 

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.  604 

249.9 

97.3 

240.3:224.6 

225 

1.068 

1 .067 

9 

53-4 

26 

15 

14.43 

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248.2 

99-3 

182.2 

171. 2 

171-3 

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1 .064 

Or 

ifice 

(03). 

I 

116. 1 

63.8 

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164.  2 

96.7 

312.5 

324-4 

329-3 

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2 

96 

51 

-II. 7 

14 

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149 

96.5 

291.4 

273 

278-5 

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3 

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14 

3 

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246 

97.2 

303-5 

290.7 

293-9 

I  .044 

1.032 

6 

113 

61.7 

62.  7 

14 

35 

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296.7 

97.6 

327 

314 

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7 

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05  .  3 

69.7 

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35 

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.  630 

369.9 

97.3 

318.9 

306.3 

320.2 

1 .042 

-995 

8 

115.4 

88.7 

91-3 

14.35 

.814 

.800 

306.  2 

96.6 

274-9 

280.6 

327.8 

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■  838 

R 

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of    P 

rofess 
Or 

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ifice 

abody' 
(bi). 

s  Expe 

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ts. 

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2 

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281.7 

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213 

207.8 

215 

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•99 

3 

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284.5 

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216 

211  .4 

220 

1 .022 

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4 

75-9 

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20.4 

14.7 

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283-4 

99-7 

228 

219.3 

227 

1.04 

1 .004 

5 

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Or 

ifice 

(62). 

I 

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99-7 

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2 

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288 

99-5 

223.5 

211. 7 

219 

I .056  I .02 

3 

72.0 

39 

24.7 

14.8 

■  452 

.616 

291 . 2 

99-5 

223 

213. 1 

220 

1 .046  I  .013 

4 

73.1 

39.2 

29.9 

14.8 

.509 

.61S 

2934 

99-5 

225.5 

213 

222 

I  .054  1 .015 

Or 

ifice 

(i-s). 

I 

72.6 

30.1 

24.8 

14.9 

.454 

.  583 

288.8 

99.6 

22s 

213.5 

220 

I .054  1 .022 

2 

72.6 

36.1 

19.9 

14-9 

.398 

.583 

286.9 

99.6 

225 

213.5 

220 

1 .054  1 .022 

3 

72.7 

36.2 

14-9 

14-8 

.339 

.583 

282.9 

99.6 

227 

213 

220 

1 .066 

1 .031 

4 

126.3 

09 

27.8 

14.7 

-29s 

■  594 

311 

99.5 

358.8 

338.9 

355 

1.058 

1 .01 

5 

125 

67.9 

40.8 

14.7 

-398 

.598 

314.6 

99-9 

355 

334-8 

352 

I  .06 

1 .01 

Res 

ults  0 

f  E.XP 

erime 
Or 

nts   b 
ifice 

y    Mic 
(c). 

kle   an 

d   Ku 

hn. 

I 

87.9 

43-4 

12 

14. 5 

■  259 

-57 

97-8 

877.3 

1042. 2 

.841 

2 

85.3 

46.8 

32.1 

14 

5 

.468 

.617 

97.8 

708.1 

3 

92.9 

48.5 

37 

14 

5 

.171 

.588 

97 

1097. I 

1093. I 

1.003 

4 

78.9 

36.6 

.74 

14 

5 

.161 

.6 

98.4 

867 

950.6 

.912 

S 

36.5 

25-3 

-2.27 

14 

5 

•  174 

-  560 

98 -5 

708 

722.6 

.979 

6 

3()-2 

13-4 

-S.68 

14 

3 

-174 

-55 

99-7 

476.3 

S16 

•  923 

7 

16.1 

.  I 

-8.8 

^ 

14 

5 

.183 

-48 

1 00.0 

295.3 

311. 4 

.948 

102 


STEAM-T  URBINES. 


0.1 


JO^ 


<^/%^_ 


FIG.  1 


\~4i Wi -> 


i"~^l 


_1.-^ 


as 


i'-^< — im"   \<  -1-^ 


t— ; 


::i? 


6i 


■/wyi 


FIG.  2 

Z>2 


.X-^K> 


J'« 


'"■^  \m         / 


FIG.  3 


ORIFICES  FOR  EXPERIMENTS  ON   P.  101, 


PLATE  VII. 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM.  103 

square  or  sharp  corners.  The  niaxinmm  rate  of  flow  is  reached 
much  more  quickly  in  some  cases  than  in  others,  as  is  shown 
by  Plates  lY,  V,  and  VI. 

Orifices  and  nozzles  having  well-rounded  entrances  Vv-ill 
pass  more  steam  than  those  with  sharp-cornered  entrances, 
but  this  does  not  mean  that  they  will  emit  a  stream  or  jet 
having  a  correspondingly  greater  velocity  than  the  latter. 
It  seems  that  the  rounded  or  bell-shaped  inlet  may  cause  a 
larger  amount  of  steam  to  be  admitted  than  can  be  efficiently 
exjianded  in  the  nozzle,  and  that  a  nozzle  having  its  entrance 
only  slightly  rounded  may  have  a  higher  efficiency  than  one 
with  a  large  convergence  of  inlet. 

In  general,  the  shape  of  the  inlet  has  greater  influence 
upon  the  rate  of  discharge  than  has  that  of  the  outlet;  while 
the  outlet  end  has  more  influence  upon  the  efficiency  of  expan- 
sion of  the  steam,  and  hence  upon  its  exit  velocity.  The 
experimental  work  to  be  discussed  later  bears  out  these  state- 
ments. 

Whether  or  not  the  weight  of  steam  flowing  through  ori- 
fices and  passages  of  large  size  and  more  or  less  irregular 
shape  can  be  calculated  as  satisfactorily  as  for  the  compara- 
tively small  sizes  that  have  been  used  in  experiments  is  not 
certain.  The  ([uantity  of  steam  that  will  flow  through  a  hole 
one  square  inch  in  cross-sectional  area,  for  instance,  is  so  great 
that  experiments  with  such  large  orifices  are  seldom  made. 
However,  the  experiments  of  Professor  Rateau,  and  of  Mr. 
George  Wilson,  given  in  the  tables  on  j)ages  106  and  109,  were 
made  with  openings  from  about  h  inch  diameter  up  to  over 
an  inch.  Unless  the  source  of  steam-supply  is  of  great  capacity, 
experiments  wuth  openings  of  large  area  are  of  necessity  made 
with  comparatively  low  pressures. 

Plate  Mil  gives  velocities  calculated  from  the  reactions 
measured  by  Mr.  George  Wilson  (London  Engineering,  1872). 
The  rate  of  flow  was  taken  from  the  curve  on  Plate  X. 
The  inlet  side  of  the  orifices  was  made  in  the  shape  of  what  is 
called   the   "contracted  vein,"   with   the  idea  of  passing  the 


104 


STEAM-TURBINES. 


PLATE  VIII. 


Initial  Pressure  of  Steam,  Pounds  Absolute  per  Sq.  In. 
rO        20       30        40       50       CO        70       80       90       100       110      130 


3000 
2800 
2600 
2400 
2200 
2000 
1800 
1600 
1100 
1200 

A 

^ 

<y 

^ 

Cros? 

Secti 

)nal  i 

rea  1. 

096  Sq 

Ins. 

B 

^ 

i. 

i 

// 
^ 

\ 

/ 

i 

i 

1^ 

^ 

' 

1 

^ 

3C00 
2800 
2600 
2400 

,. — ■ 

-A 

^' 

_-o— 

Gro — o 

-^c 

^ 

f\ 

r^ 

2C00 
1800 
1600 
1400 
1200 

/ 

y 

Cr 

JssSe 

3tiona 

Ares 

.4869 

3q.  In 

s. 

^ 

/ 

^-t-           1 

; 

•3 

i 

d 
) 

a. 

V 

V 

; 

10        20       30        40        50       60        TO       80        90      100      110      120 

Initial  Pressure  of  Steam,  Pounds  Absolute  per  Sq.  In. 

Curves  A  give  velocity  under  ideal  conditions  of  steam-flow  into  the 
atmosphere. 

Curves  B  and  C  give  calculated  velocity  as  indicated  by  measured  re- 
action.    From  experiments  by  Mr.  George  Wilson. 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM.  105 

greatest  possible  volume  of  steam.  The  orifices  were  of  com- 
paratively large  size  (2  and  3  centimeters  diam.  respectively), 
and  it  may  be  that  the  weight  of  steam  discharged  per  second 
was  somewhat  greater  than  that  calculated  and  used  in  finding 
the  A^elocity  from  the  reaction.  That  would  account,  at  least, 
for  the  calculated  velocity  being  somewhat  above  that  given 
by  the  ideal  curves  A,  because  the  velocity  is  calculated  from  the 
equation 

RXS2.2 


V  = 


W 


and  therefore  varies  inversely  as  the  weight  of  flow,  W.  How- 
ever the  curves  show  the  same  characteristics  as  the  other 
results  given  for  orifices  and  straight  tubes,  namely,  a  decided 
falling  off  in  velocity  for  initial  pressure  above  70  or  80  pounds 
absolute,  and  comparatively  high  velocities  for  pressures  lower 
than  70  or  80  pounds. 

Further,  comparing  these  curves  with  those  from  small 
nozzles  for  which  the  velocity  has  been  determined  by  measure- 
ment of  both  reaction  and  weight  of  flow  (see  page  125),  it 
seems  safe  to  conclude  that  the  velocities  given  on  Plate  VIII 
are  not  more  than  from  10  to  15  per  cent  too  high,  if  indeed  they 
are  as  much  as  that  above  the  actual  values.  The  surface  of 
the  orifice,  causing  frictional  resistance  to  flow,  increases  only 
as  the  diameter  of  orifice,  while  the  quantity  of  steam  increases 
as  the  square  of  the  diameter.  It  is  therefore  probable  that 
with  large  orifices  of  favorable  shape  the  frictional  losses  are 
proportionately  less  than  with  small  orifices  and  nozzles,  antl 
that  the  high  velocities  indicated  by  the  curves  B  and  C  were 
more  closely  realized  than  comparisons  with  results  from  smaller 
orifices  and  nozzles  would  lead  one  to  believe. 

The  calculated  results  in  the  following  table  agree  more 
closely  with  observed  results  in  the  case  of  the  convergent 
nozzles  than  in  that  of  the  orifice  in  the  thin  plate.  The  con- 
vergent nozzles  were  simply  orifices  with  bell-shaped  entrances, 
and  it  was  shown  on  page  99  that  the  equations  for  weight  of 


106 


STEAM-TURBINES 


discharge  apply  more  closely  to  such  orifices  than  to  those  with 
sharp-cornered  entrances. 

Results  op  Experiments  by  Professor  Rateau,  and  Calculations 

FROM  Them. 


A,  convergent  nozzle.  B,  orifice  in  tliin  plate. 


A  large  amount  of  data  on  the  pressures  existing  at  different 
points  along  steam-nozzles,  and  in  jets  from  orifices,  has  been 
obtained  by  experiments,  and  such  information  has  thrown  a 
considerable  amount  of  light  on  turbine  operation.  But  given 
that  sort  of  data  alone,  designers  are  almost  as  much  at  sea  as 
before  regarding  the  true  efficiency  of  a  nozzle  or  steam-passage 
and  the  actual  velocity  of  steam-jets. 

The  experimental  work  giving  the  most  direct  and  satis- 
factory evidence  concerning  the  efficiency  of  steam-flow  in 
nozzles  and  orifices  has  been  that  determining  the  reaction  of 
the  jet  against  the  vessel  from  which  it  flows. 

The  work  of  Mr.  George  Wilson  (see  London  Engineering, 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM.  107 

Vol.  XIII,  1872)  and  of  Mr.  Walter  Rosenhain  (see  Proc.  Inst.  C.  E., 
London,  1899)  was  of  this  character,  and  in  both  cases  the  experi- 
ments were  evidently  made  with  care.  Mr.  Wilson's  apparatus 
is  shown  on  p.  140.  He  (Ud  not  measure  the  quantity  of  steam 
discharged,  but  did  obtain  a  measure  of  the  reaction  accompany- 
ing discharge,  under  various  initial  pressures,  into  the  atmos- 
phere, with  the  various  orifices  which  he  employed.  The  sec- 
ond table  on  page  109  gives  a  few  of  Mr.  Wilson's  results  for  the 
purpose  of  comparing  the  observed  reactions  with  those  given 
by  the  use  of  the  equation  developed  in  the  following  pages. 

Mr.  Walter  Rosenhain,  of  the  University  of  Cambridge, 
has  gone  a  step  farther  than  did  Mr.  Wilson,  as  he  has  measured 
both  the  reaction  and  the  rate  of  steam-flow.  Mr.  Rosenhain's 
experiments  cover  a  wide  range  of  initial  pressures,  but  the 
final  pressure  is  that  of  the  atmosphere  in  all  the  experiments, 
as  was  the  case  with  Mr.  Wilson's  experiments. 

Experiments  are  at  the  present  time  being  carried  on  in 
Sibley  College,  in  which  the  reaction  and  weight  of  flow  are  meas- 
ured, and  in  which  the  back  pressure  is  carried  down  below 
the  atmospheric  pressure,  as  is  the  case  in  all  condensing  turbine 
plants.  It  is  the  purpose  of  the  experiments  to  measure  the 
heat  in  the  discharge  from  nozzles  in  w^hich  known  kinetic 
energy  is  developed,  per  pound  of  steam  supplied,  and  thus  to 
find  the  efficiency  of  the  nozzles  when  discharging  into  the 
vacuum  in  the  condenser. 

Mr.  Rosenhain's  apparatus  is  shown  in  Figs.  27-29,  and 
the  first  table  on  page  109  gives  calculations  based  upon  the 
flow  from  the  simple  orifice.  No.  1. 

These  results  are  given  to  show  the  degree  of  approximation 
to  be  attained  by  the  use  of  the  equations  for  calculating  the 
weight  of  flow  and  the  reaction  as  explained  in  Chapter  IV.  The 
velocities  as  calculated  are  also  given,  and  all  the  variables  are 
further  represented  in  the  curves  plotted  on  Figs.  30-40. 

These  experiments  are  of  great  importance  in  at  least  par- 
tially answering  the  questions  stated  on  page  93.  It  is  hoped 
that  before  long  experimental  results  giving  further  information 


108 


STEAM-TURBINES. 


Fig.  29. 


Hood  for  collecting  steam  and  directing  it  to  condenser. 
Mr   Rosenhain's  apparatus. 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


109 


will  be  available,  especially  regarding  the  flow  into  condensers 
maintaining  conditions  of  vacuum. 

Experiments  by  Mr.  Walter  Rosenhain.* 


p. 

Weight  Flov 

•  per  Second. 

Velocity 

of  Efflux. 

'S'o.cP 

>   cJ,^^ 

Pressure, 

Initial 

Pounils  per 

Square  Inch. 

Calculated. 

Actual. 

Calculated 

from 
Calculated 
Reaction. 

Calculated 

from 

Actual 

Reaction. 

^J2  1  • 

26 

0.0105 

■^^'-^iZ 

35 

0  0137 

0.0137 

1770 

1580 

-  O    C    II    G 

55 

0.0222 

0.0220 

2010 

1900 

R   ■■"  -  •: 

75 

95 

115 

0.0287 
0.0364 
0.04.30 

0.0290 
0.0370 
0 . 0440 

2250 
2410 
2470 

2100 
2250 
2350 

lin  pla 
rectioi 
75  si\. 
reactio 
squan 

135 

0.0511 

0.0510 

2520 

2450 

155 

0.0587 

0.05.S0 

2560 

2530 

_=  .  3  ^  a 

175 

0.0656 

0.0640 

2610 

2580 

8'H  p-2-3 

195 

0.0726 

0.0720 

2650 

2620 

S^S-55 

215 

0.0805 

0.0780 

2660 

2650 

5  o  g^  2 

Mr.  George  Wilson's  Experiments. 


Area  of 
Orifice, 
Square 
Inches. 

Absolute 

Initial 
Pressure. 

Calculated 
Weight 
of  Flow. 

Calculated 
Reaction, 
Pounds. 

Actual 
Reaction, 
Pounds. 

Calculated  Velocity. 

Diameter 

of  Orifice, 

Inches. 

From 
Actual 
Reaction 
and  Calcu- 
lated 
Weight 
of  Flow. 

From 

Calculated 

Reaction 

and 
Weight 
of  Flow, 
Ft.  Sec. 

0.787 

0.487 

114.0 

0.785 

61.0 

59.6 

2450 

2580 

( I 

" 

108.0 

0.755 

57.5 

56.2 

2400 

2.520 

1 1 

" 

97.0 

0.680 

51.0 

50.8 

2400 

2510 

1 1 

" 

88.0 

0.614 

45.0 

46.4 

2440 

2475 

li 

' ' 

78.0 

0.550 

39.5 

40.2 

2360 

2390 

1.18 

1.096 

73.5 

1.27 

83.0 

85.1 

2160 

2350 

( ( 

<  ( 

67.0 

1.18 

74.0 

76.3 

2080 

2280 

( i 

i  1 

61.0 

1.05 

66.0 

67.0 

2050 

2290 

1 1 

1 1 

56.0 

0.965 

59.0 

61.2 

2050 

2210 

1 1 

51.0 

0.890 

53.0 

53.8 

1950 

2130 

The  calculated  reaction  given  in  the  above  tables  was  obtained  by  the 
use  of  the  empirical  formula  developed  on  page  74,  Chapter  V,  for  jets  dis- 
charging into  the  atmosphere.     Thus, 

Reaction  =  E  =  (1.23Pi  — 14.7)  pounds  per  square  inch  of  orifice. 

*  Reviewed  by  permission  of  Mr.  Rosenhaie 


110  STEAM-TURBINES. 

Mr.  Rosenhain  starts  with  the  premise  justified  both  by 
theory  and  by  experiment,  that  with  a  constant  upper  pres- 
sure a  limiting  velocity  of  efflux  is  reached  when  the  lower 
pressure  has  been  reduced  to  between  50  and  60  per  cent  of 
the  higher  pressure,  while  no  limiting  value  is  indicated  when, 
with  a  constant  low  pressure,  the  higher  pressure  is  increased. 
This  does  not  apply  to  conically  divergent  nozzles,  and  the 
theoretical  conclusions  apply  only  to  the  narrowest  section 
of  a  nozzle.  The  experimental  conclusions  apply  only  to 
orifices  in  thin  plates  or  convergent  nozzles  of  various  types, 
including  short  cylindrical  tubes. 

Profiting  by  the  records  of  previous  experiments  he  de- 
cided that  it  would  be  desirable  to  measure  the  velocity  of 
the  steam  as  directly  as  possible,  and  to  avoid  estimating  the 
density  of  the  steam  at  the  point  of  efflux.  This  estimation, 
depending  upon  temperature  measurements,  admits  the  greatest 
liability  to  error.  Moreover,  the  velocity  required  for  steam- 
turl^ine  purposes  is  the  actual  velocity  attained  by  the  steam  on 
leaving  the  nozzle,  not  merely  a  figure  in  feet  per  second  from 
which  the  mass  discharged  could  be  calculated  when  the  area 
of  the  orifice  and  the  density  of  the  steam  are  known.  He 
found  it  necessary,  therefore,  to  measure  both  the  mass  dis- 
charged and  another  quantity  involving  the  velocity.  For 
this  second  quantity  he  chose  the  momentum  of  the  escaping 
jet.  He  first  tried  to  measure  this  momentum  by  allowing 
the  jet  to  impinge  upon  a  semi-cylindrical  bucket  or  vane  in 
such  a  way  as  to  reverse  the  jet,  estimating  that  the  pressure 
on  the  vane  should  then  be  equal  to  twice  the  momentum 
given  to  the  jet  per  second.  This  method  did  not  prove  satis- 
factory and  was  rejected.  He  then  adopted  the  reaction 
method. 

Various  methods  of  using  the  apparatus  were  tried,  and, 
as  a  means  of  verifying  the  observations  obtained  by  other 
methods,  the  method  was  adopted  of  obtaining  the  desired 
pressure  at  the  gage  by  throtthng  the  steam  at  the  valve. 
The  only  observable  difference  he  found  between  the  jet  at 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


Ill 


20  40  60  80  100         120         140         160         180         800 

Pressure  of  steam  in  lbs.  per  square  inch. 
Fig.  30. 


112  STEAM-TURBINES. 

full  way  and  by  throttling  to  the  same  pressure  was  in  the 
appearance  of  the  jet.  The  throttled  jet,  when  the  throttling 
was  considerable— as  from  200  pds.  per  square  inch  to  20  lbs. 
per  square  inch— was  of  a  darker  color,  much  more  trans- 
parent, but  showing  the  brown  color  by  transmitted  light 
much  more  strongly;  at  the  same  pressure  not  the  slightest 
difference  in  reaction  could  be  observed  between  a  "full- way" 
and  a  "throttled"  jet. 

The  nozzles  shown  in  section  in  Fig.  28  were  of  gun-metal, 
and  were  carefully  prepared  to  exact  dimensions.     No.  I  is  an 
orifice  in  a  thin  plate,  produced  by  a  very  oblique  chamfer  on 
the  outside.     No.  II  consists  of  two  parts  drilled  and  turned 
up  together.     A\\  the  experiments  with  this  nozzle  as  a  whole 
were  completed  before  the  parts  were  separated   to  form  the 
new  nozzles  IIa  and  IIb.      Nos.  Ill  and  IV  were  made  of 
approximately  the  same  length  as  IIb,  and  with  larger  and 
smaller  tapers  respectively.     No.  Ill  was  then  cut  down  to 
form  III  A,  the  greatest  diameter  of  which  is  equal  to  that  of 
IV.     Finally,  IIIa  was  also  cut  down  to  form  IIIb.     No.  IV 
was  also  cut  down  by  |  inch  at  a  time  to  form  IVa,  IVb,  IVc, 
and  IVd  successively.     In  III  and  IV  the  inner  edge  of  the 
nozzle  is  merely  rounded  off  smoothly.     These  were  designed 
on  lines  suggested  by  the  results  of  the  experiments  on  II,  IIa, 
and  IIb.     The  area  of  the  orifice  or  nozzle  does  not  enter  into 
the  calculation  of  the  velocity.     In  order,  however,  to  make 
the  results  strictly  comparable,  the  entire  set  of  nozzles  was 
made  with  as  nearly  as  possible  the  same  least  diameter,  A  inch. 
This  diameter   and  the  tapers  approximate  to   those  used  on 
a,  De  Laval  5-H.P.  turbine-motor.     A  table  showing  the  dimen- 
sions of  the  nozzles  as  supphed  with  this  turbine  is  given  on  page 
114,  for  the  sake  of  comparison.     The  actual  least  diameter 
of  each  nozzle  was  carefully  measured  with  a  micrometer  micro- 
scope to  an  accuracy  of  0.001  inch. 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM  113 


Fig.  31. 

Pressure  of  Steam  in  Lbs.  per  Square  Inch. 
20  40  00  80         K«         IJO         140  100        180        20Q,inA 


!W  40  00  80  100  120         140  100  180  200 

Pressure  of  Steam  in  Lbs.  per  Square  Inch 
Fig.  32. 


114 


STEAM-TURBINES. 


Ex 

PERiMEXT.\L  Nozzles. 

Number. 

Lea-st 
Diameter. 

Greatest 
Diameter. 

Length. 

Taper. 

Remarks. 

I 

Inches. 
0 . 1873 
0 .  1840 
0.1866 
0.1849 
0 . 1882 
0.1882 
0 .  1882 
0.1830 
0 . 1830 
0.1830 
0.1830 
0.1830 

Inches. 

Inches. 

Orifice  in  thin  plate 
Compound  nozzle 
Inlet  half  of  II 
Outlet  h&lf  of  II 

}  Inlet  edges  slightly  rounded 

1 

II 

IIa 

IIb 

III 

IIIa 

IIIb 

IV 

IVb 

iVc 
I^'d 

0.287 

0.287 
0.368 
0.255 
0.241 
0.255 
0.242 
0.230 
0.217 
0.205 

2.1 

0.5 

1.6 

2.16 

0.79 

0.64 

2.16 

1.785 

1.41 

1.035 

0.66 

1  in  20 

1  in  20 
1  in  12 
1  in  12 
1  in  12 
1  in  30 
1  in  30 
1  in  30 
1  in  30 
1  in  30 

De  L.\.v.\.l  Nozzles  for  5-Horse-power  Turbine. 


Pressure. 

Least  Diameter. 

Length. 

Taper. 

Poimds  per  Square  Inch. 

Inch. 

Inch. 

136 

0.157 

1.57 

1  in  17.4 

105 

0.163 

1.57 

1  in  21.4 

Experiment  IIb 

0.184 

2.11 

1  in  20.0 

100 

0.197 

1.57 

1  in  19.0 

60 

0.230 

1.57 

1  in  29.0 

58 

0.256 

1.57 

1  in  26.6 

The  formula  used  for  the  calculation  of  the  velocity  of  the 
steam  in  the  jet  is 

"  W ' 


Y 


where  T'  is  the  velocity  of  the  steam  in  feet  per  second; 
R  is  the  reaction  in  lbs.  weight ; 
g  is  the  acceleration  of  gravity  taken  at  32.2  feet  per 

second  per  second; 
W  is  the  weight  of  steam  discharged  in  lbs. 
From  the  description  of  the  experiments  it  will  be  seen 
that  R  and  TT^  are  measured  directly.      For  purposes  of  calcu- 
lation, points  were  plotted  on  squared  paper  showdng  for  each 

nozzle 

(a)  Steam  pressure  as  abscissa,  R  as  ordinate; 

(6)  Steam  pressure  as  abscissa,  W  as  ordinate. 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


115 


From  the  smooth  curves  drawn  to  represent  these  points 
values  of  IF  and  R  were  taken  and  used  in  the  above  formula 


Discharge  in  lbs.  per  second 


Discharee  in  lbs.  per  second 

to  give  values  of  V ;   and,  finally,  a  third  curve  was  plotted, 
showing 

(c)  Steam  pressure  as  abscissa,  V  as  ordinate. 

This  last  curve  represents  the  relation  between  pressure  and 


116 


STEAM-TURBINES. 


velocity,  and  also  serves  as  a  check  on  the  accuracy  of  the 
arithmetical  calculations. 

The  formula  used  assumes  that  at  the  point  where  the 
velocity  is  measured  the  steam  has  reached  atmospheric  pres- 
sure, otherwise  the  reaction  would  be  increased  by  the  remain- 
ing pressure;  that  is,  the  velocity  here  determined  is  that 
which  the  steam  attains  on  reaching  atmospheric  pressure 
where  this  occurs  outside  the  nozzle,  or  its  velocity  on  leaving 


.U'J 

IV,Ivk,IVB  & 

.08 

y/O^lMX, 

.or 

a 
o 
c 

o^ 

y 

^.00 

J^ 

P< 

^ 

^.05 

r^ 

f 

® 
M.04 

cS 
,£3 

5.03 

?^ 

/> 

r 

X 

.02 
.01 

y 

^ 

T 

10  30  50  70  90  110  130  150  170  190  210 

Pressure  of  steam  1n  lbs.  per  square  inch 

Fig.  35. 

the  nozzle  where  atmospheric  pressure  has  been  attained 
within  the  nozzle,  in  which  case  friction  against  the  nozzle 
after  complete  expansion  has  occurred  may  cause  the  steam 
to  lose  some  of  its  momentum.  For  practical  purposes  Mr. 
Rosenhain  assumes  that  the  velocities  here  found  correspond 
to  the  kinetic  energy  of  the  jet  on  leaving  the  nozzle,  an 
assumption  which  he  found  justified  by  observations  on  the 
shape  of  the  jets.  With  the  exception  of  those  from  the  two 
very  short  nozzles.  No.  IIIb  and  No.  IVd,  the  jets,—  even  that 
from  No.  I, — are  very  nearly  parallel  for  several  inches  from 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 
Calculated  velocity  in  feet  per  second. 


ii: 


Calculated  velocity  in  feet  per  second. 


118  STEAM-TURBINES. 

the  end  of  the  nozzle,  or  at  most  diverge  at  approximately  the 
same  taper  as  the  nozzle. 

In  the  case  of  the  expanding  nozzles  this  shows  that  the 
steam  is  expanded  to  atmospheric  pressure  before  leaving  the 
apparatus. 

The  first  series  of  curves,  Figs.  30,  33,  and  36,  represent  the 
experiments  made  with  nozzles  Nos.  I,  II,  IIa,  and  IIb.  The 
reaction  curves,  Fig.  30,  are  mostly  straight  lines,  i.e.,  the  reac- 
tion is  simply  proportional  to  the  pressure,  but  the  constants 
vary  for  different  nozzles.  In  the  case  of  No.  I,  the  orifice  in 
a  thin  plate,  the  curve  is  a  straight  line  through  the  origin, 
while  for  all  other  nozzles  the  hne  could  reach  the  origin 
only  through  a  curve.  With  IIa  there  is  a  sUght  but  distinct 
sinuosity  in  this  curve,  and  the  points  of  IIb  show  a  tendency 
to  something  similar.  Mr.  Rosenhain  verified  this  by  repeat- 
ing the  experiments  under  different  conditions.  He  assigns 
the  cause  of  the  peculiarity  to  friction,  as  the  sinuosity  occurs 
only  in  those  two  nozzles  where  the  friction  would  be  large. 
It  should  be  remembered,  in  comparing  the  curves,  that  the 
minimum  diameters  of  II,  IIa,  and  IIb  are  identical,  but 
that  of  I  differs  very  slightly. 

The  discharge  curves  (Fig.  33)  occupy  natural  positions. 
The  nozzle  having  an  easy  inlet  and  an  expanding  outlet  gives 
the  greatest  discharge,  the  inlet  being  evidently  more  important 
than  the  outlet,  hence  the  near  approach  of  IIa  to  I. 

The  position  of  IIb  so  far  below  I  would  seem  to  justify 
Mr.  Rosenhain's  conclusion  that  "  the  sharp  inlet  is  unsuited 
to  passing  a  large  quantity  of  steam  through  an  expanding 
nozzle;  while,  on  the  other  hand,  the  velocity  curves  (Fig.  36) 
show  that  the  ciuantity  of  steam  passed  by  a  nozzle  depends 
very  considerably  on  the  shape  of  the  inlet,  and  the  velocity 
of  the  steam  on  leaving  the  nozzle  depends  more  on  the  shape 
of  the  outlet  portion." 

From  this  he  concludes  that  the  density  of  the  steam  at 
the  narrowest  section  depends  upon  the  shape  of  the  inlet, 
and  that  "  this  density  for  a  given  internal  pressure  is  greater 


EXPERIMENTAL   WORK  OX  FLOW  OF  STEAM.  119 

Calculated  velocity  in  feet  per  second 


Calculated  velocity  in  feet  per  second 


120  STEAM-TURBINES. 

with  a  well-rounded  inlet  than  with  a  nozzle  having  a  sharp 
inner  edge." 

This  would  account  at  once  for  the  most  conspicuous  feature 
of  this  set  of  velocity  curves,  viz.,  that  up  to  a  pressure  of 
about  80  lbs.  per  square  inch  the  greatest  velocity  is  attained 
by  a  jet  from  an  orifice  with  a  thin  plate;  above  100  lbs. 
per  sq.  inch,  IIb,  having  a  sharp  inlet,  gives  a  greater  velocity 
than  II,  which  has  a  rounded  inlet  and  the  same  outlet.  So 
that  apparently  a  rounded  inlet  admits  a  greater  weight  of 
steam  to  the  narrowest  section  than  the  nozzle  can  deal  with 
efficiently.  Thus,  the  advantage  of  I  over  IIa  arises  from 
its  smaller  discharge,  which  can  expand  with  greater  freedom 
and  so  develop  a  greater  velocity  than  the  denser  steam  issuing 
from  IIa. 

Considering  the  kinetic  energy  developed  per  pound  of 
steam,  the  velocity  curves  may  be  taken  to  represent  the 
"  efficiency "  of  the  various  nozzles.  From  that  point  of 
view,  Mr.  Rosenhain  concludes:  "The  effect  of  a  sharp  inlet 
is  to  reduce  the  density  of  the  steam  at  the  narrowest  section, 
and  hence  less  steam  is  passed,  but  the  steam  that  does  pass 
is  fully  or  almost  fully  expanded;  hence,  though  the  dis- 
charge is  reduced,  the  efficiency  is  increased." 

In  consequence  of  this  conclusion,  he  designed  all  the  later 
nozzles  with  an  inner  edge  only  slightly  rounded  off. 

Nozzle  IV  was  cut  down  by  small  steps,  f"  being  taken 
off  the  length  each  time,  thus  producing  nozzles  IVa,  IVb, 
IVc  and  IVd.  Figs.  32,  35,  and  39  show  the  reaction^ 
discharge,  and  velocity  at  the  nozzles.  In  order  to  present 
the  results  more  clearly  the  curves  of  Fig.  40  were  plotted. 
Here  the  length  of  nozzle  is  taken  as  abscissa,  and  reaction, 
discharge,  and  velocity  are  taken  as  ordinates  for  separate 
curves  which  have  been  plotted  for  steam  pressures  of  50, 
100,  150,  and  200  pounds  (by  gage)  pressure  respectively. 
"  These  curves  show  that  reaction  and  discharge  are  influenced 
by  the  length  of  the  nozzle  in  opposite  ways.  Very  long  nozzles 
with  low  steam  pressui'e,  or,  more  generally,  nozzles  that  tend 


EXPERIMENTAL  WORK  ON  FLOW   OF  STEAM. 


121 


Nozzles 
rV'D    JVC    IVB    IVA    IV       IVD    IVC     IVC   IVA    IV  IVD  IVC    IVB    IVA     IV 


■— 

.08 
.07 

.00 

-d 

a 
o 
o 

s. 

jQ 

.3.05 

9) 

d 
.a 
o 
tn 

S 
.04 

.03 
.0-2 

/ 

Velocity  in  feet  per  second 

^ 

/ 

/ 

/ 

/ 

/ 

l^ 

/ 

/ 

/ 

/ 

•-''^ 

y 

y 

/ 

^ 

^ 

^ 

V 

\^ 

y 

N 

^ 

^ 

\ 

V 

\ 

^ 

\ 

\ 

Fig.  40. 


122  STEAM-TURBINES. 

to  cause  over-expansion,  produce  a  large  discharge  but  com- 
paratively small  reaction." 

Considering  further  the  question  of  "  efficiency "  in  the 
sense  just  defined,  it  will  be  seen  that  the  most  efficient  form 
of  nozzle  varies  with  the  pressure.  The  reaction  curve  at 
100  lbs.  per  square  inch  shows  a  maximum  at  IVa  which 
recurs  much  more  markedly  in  the  corresponding  velocity 
curve.  The  shape  of  the  curve  at  50  lbs.  per  square  inch 
indicates  that  for  these  low  pressures  a  long  expanding  cone  is 
distinctly  bad;  in  fact,  a  comparison  of  Figs.  36,  37,  38,  and 
39  shows  that  up  to  80  lbs.  per  square  inch  an  orifice  in  a 
thin  plate  is  more  efficient  than  any  form  of  nozzle  used  in 
these  experiments. 

At  100  lbs.  per  square  inch  the  velocity  curve  shows  both 
a  maximum  and  a  minimum.  A  maximum  was  to  be  expected; 
the  minimum  would  seem  to  indicate  that  the  increase  of 
length  from  IA"d  to  lYc  brings  the  discharge  up  to  the  high- 
est value  attainable  for  this  pressure,  while  neither  H'c  nor 
IVb  is  long  enough  to  develop  the  full  reaction.  Again, 
the  fall  in  the  velocity  curve  from  IVa  to  lY  he  attributes 
to  "  over-expansion,"  especially  as  it  disappears  at  150  lbs. 
per  sq.  inch.  Here  the  minimum  has  moved  towards  IVd, 
and  it  practically  disappears  at  200  lbs.  per  square  inch.  At 
150  lbs.  per  square  inch  IV  seems  just  to  touch  the  maximum 
velocity  attainable  by  a  nozzle  of  that  taper,  while  for  200 
lbs.  per  sq.  inch,  even  IV  may  be  said  to  give  insufficient 
expansion. 

As  a  guide  to  the  design  of  the  most  efficient  nozzle,  then — ■ 
that  is,  the  one  that  will  develop  the  greatest  kinetic  energy 
in  the  jet  per  pound  of  steam  consumed — Mr.  Rosenhain  sum- 
marizes the  results  of  the  experiments  as  follows: 

"Up  to  a  boiler  pressure  of  about  80  lbs.  per  square  inch, 
and  for  discharge  into  atmospheric  pressure,  the  most  efficient 
form  is  an  orifice  in  a  thin  plate.  For  higher  boiler  pressures 
an  expanding  conical  nozzle  ^^•ith  an  inner  edge  only  slightly 
rounded  should  be  used.     The  taper  should  not  be  very  different 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM.  123 

from  1  in  12,  and  the  proper  ratio  of  greatest  and  least  diameters 
is  given,  according  to  present  results,  in  the  follomng  table: 


Steam  pressure,  lbs.  per  sq.  inch,  gage . 

80 

100 

140 

160-200 

Ratio  of  d  ameters 

1.26 

1.26-1.33 

1.36 

1  36 

"The  bearing  of  the  above  resuhs  on  the  thermohydro- 
dynaniic  equation  of  Weisbach  is  not  very  direct.  The  i)art 
played  by  friction  in  these  nozzles  is  very  great  and  can  only 
be  allowed  for  in  the  equations  by  the  introduction  of  artificial 
coefficients,  and  these  hardly  seem  worth  calculating,  especially 
as  it  seems  doubtful  if  hydrodynamic  equations  are  applicable 
to  gases.  Hydrodynamics  is  based  on  the  assumption  of  a 
perfectly  homogeneous  fluid,  but  a  gas,  and  still  less  a  vapor 
carrying  particles  of  water  in  suspension,  does  not  satisfy  this 
condition." 

EXPERIMENTS   WITH  TURBIXE-BUCKETS. 

Extensive  experimental  turbine  work  was  done  in  the  Sibley 
College  Laboratories  during  the  years  1897-98-99,  under  the 
direction  of  Mr.  Thomas  Hall  of  the  class  of  1894,  one  of  the 
designers  of  the  Hall  and  Tre.at  quadruple  expansion  engine. 
Mr.  Hall  held  the  Sibley  Fellowship  during  1894-95,  and  was 
subsequently  an  instructor  for  two  years.  During  this  latter 
period  he  superintended  the  experimental  work  discussed  in  the 
follo^^'ing  pages,  and  to  his  efforts,  supplemented  b}'  the  effi- 
cient work  of  ^Messrs.  Rathbons  and  Jones,  '97-'98,  and  Messrs. 
Loetscher  and  ^McDonald,  '98-'99,  is  to  be  given  full  credit 
for  the  valuable  information  obtained.  The  curves  presented 
here  have  been  plotted  fron  the  data  obtained,  some  of  the 
curves  being  given  as  originally  plotted  by  the  investigators. 

The  points  investigated  were  as  follows: 

(a)  The  weight  of  flow  of  steam  through  nozzles  of  varying 
size  under  different  initial  steam  pressures  and  atmospheric 
exhaust  pressure. 


124  STEAM-TURBINES. 

(b)  The  actual  velocity  of  the  jet  from  the  nozzles  as  indicated 
by  the  nozzle  reaction. 

(c)  The  impulse  exerted  by  the  jet  upon  buckets  having 
various  angles  of  entrance  and  exit. 

(d)  The  impulse  as  affected  by  bucket-spacing. 

(e)  The  impulse  as  affected  by  clearance  between  the  nozzle 
and  the  buckets. 

(/)  The  impulse  as  affected  by  placing  a  varying  number  of 
rows  of  stationary  buckets  in  front  of  a  set  of  movable  buckets. 

(g)  The  impulse  as  affected  by  the  clearance  between  rows 
of  buckets 

(h)  The  substitution  of  air  for  steam,  comparing  the  im- 
pulsive pressures  upon  the  buckets  in  the  two  cases. 

(k)  The  impulse  as  affected  by  ''cutting  over"  the  edges 
of  the  buckets  by  the  jet  of  air  from  the  nozzle. 

(J)  The  efficiency  of  rough  surface  buckets  as  compared 
with  those  having  smooth  surfaces. 

The  discharge  from  nozzles  and  buckets  was  in  all  cases  at 
atmospheric  pressure.  The  nozzles  experimented  with  were  of 
diameters  I",  ,%",  I",  and  f",  2  inches  long,  with  rounded 
entrance  and  with  sharp  entrance,  and  with  straight  and  ex- 
panding bores.  The  curves  are  marked  so  as  to  show  to  what 
character  of  nozzle  they  correspond.  The  weight  of  flow  per 
second  corresponds  with  the  data  previously  given,  and  is 
given  with  other  data  for  |"  nozzles  in  Fig.  41.  The  curves 
for  the  I"  nozzles  show  that  for  initial  pressures  up  to  about  70 
pounds  absolute  the  straight  nozzles  gave  liigher  velocities  than 
the  expanding  nozzle,  but  that  above  70  pounds  the  reverse 
was  true.  However,  in  these  cases  the  jet  from  the  straight 
nozzles  acted  upon  the  buckets  more  efficiently  than  did  that 
from  the  expanding  nozzle. 

The  centers  of  the  ends  of  the  straight  and  the  expanding 
nozzles  were  placed  at  the  same  distance  from  the  buckets, 
and  since  the  jet  begins  to  diverge  in  the  bore  of  the  expand- 
ing nozzle,  and  not  until  it  has  left  the  straight  nozzle,  the 
expeiimenters  concluded  that  the  expanding  nozzles  hould  be 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEA^r. 


12c 


3000 
2S00 
•^00 
2100 
2200 
2000 
1800 
IGOO 
1400 
1300 
1000 
800 
GOO 
400 


EXPERIMENTS  WITH  V4 

DIA,  NOZZLES, 
riwivPRAlTV    1«q7_  qs 

•3 
B 
3 
O 

BY  MESSRS.  JONES  AND  RATHBONE. 

C 

Curve  A,  Reattiou,  Straight  Nozzle.  SUarp  Entrance 
,.      B           M                 "           •'      Rounded       " 
c',          '■         Expanding  "            "              " 
A,'  Velocity,  Straight       "       Sharp 
B,'         '•                "            "     Rounded       " 
'■       C'         ••          Expanding  " 
••       Dj          •■         Ideal  Conditions       "              " 

— 8 — 

075 

Q."/ 

B 

/• 

.070 

All  Nozzles  X  Least  Diam. 

'A 

c' 

0C5 

Dv^--^''^ 

-7 

000  3 

-c — 

'  .:^^^ 

-/ 

CO 

.055-i 

/ 

y 

/    J 

// 

B 

.050-1 

/ 

/J 

Y/\ 

A 

V, 

/ 

^A 

/ 

'  A 

045  r 

/ 

V\ 

/ 

// 

V 

// 

/ 

/ 

0 
040  M 

/// 

/ 

A 

V 

/y 

f. 

V 

.035 

/// 

// 

Vx 

.030 

///         /^ 

// 

'^y 

.025 

0 

/y 

^   Curve  A,  Wt.  of  Flow,  St.  Noz.  Sbarp  Ent. 

B," Round    •' 

•'       C," Exp. 

.020 

1  /  /  ///  1 

^ 

// 

.015 

t 

1 

.010 

/ 

1/  ^  ^ 

Taper  of  Expanding  Nozzle, .^^j  Increase  in  Dia. 

.005 

/ 

\/\ 

Leng 

th  of  N 

ozzles 

rsiate 

rial,  Br 

jnze. 

0 

30 


50         00        70 
Absolute  Piessun 


SO 


110        120 


Fig.  41. — Xote  the  difference  in  character  of  curves  C  and  C,  which  are 
from  the  expanding  nozzle,  from  the  curves  representing  the  straight -nozzle 
results.  The  energy  of  the  jet  from  the  expanding  nozzle  is  below  that  from 
the  straight  nozzle  up  to  about  70  pounds  absolute,  after  Which  it  goea 
above. 


126  STEAM-TURBINES. 

placed  nearer  the  buckets  than  the  straight  nozzle  for  equal 
efficiency. 

In  general,  the  impulse  upon  the  135°  buckets,  Figs.  42  and 
43,  was  somewhat  liigher  than  that  upon  the  150°  buckets.  This 
may  have  been  due  to  the  fact  that  the  latter  were  somewhat 
tliicker  than  the  former,  and  hence  had  less  space  between  them 
for  passage  of  steam.  Upon  the  basis  of  the  tests  made  and 
shown  by  the  curves,  it  was  decided  to  use  135°  buckets  in  all 
the  tests,  and  to  place  the  nozzles  at  such  an  angle  that  the 
stream  would  enter  tangentially  to  the  bucket  surfaces.  Sufh- 
cient  buckets  were  used  in  all  cases  so  that  all  the  stream  from 
the  nozzle  impinged  upon  buckets.  There  were  from  four  to 
six  buckets  used  in  each  set. 

The  general  arrangement  of  this  apparatus  used  is  given 
in  Fig.  52. 

The  clamps  for  holding  the  buckets  were  guided  and  attached 
to  the  balance  scales,  so  that  the  impulse  might  be  measured. 
The  reaction  upon  the  nozzles  was  obtained  in  a  similar  manner 
for  each  steam  pressure  employed,  and  the  rate  of  flow  at  each 
pressure  was  determined  by  a  separate  test  in  which  the  steam 
from  the  nozzle  was  led  to  a  condenser  antl  then  weighed. 
Preliminary  runs  were  made  until  the  apparatus  was  in  satis- 
factory working  order,  and  results  of  subsequent  runs  were 
carefully  checked  by  repeating  the  experiments. 

In  each  series  of  impulse  tests  the  steam  pressure  was 
increased  by  increments  of  10  pounds  up  to  100  pounds  gage 
pressure.  The  method  of  weighing  the  impulse  proved  to  be 
very  delicate,  and  the  accuracy  of  the  results  is  shown  by  the 
regularity  with  wliich  they  plot  into  smooth  curves. 

Spacing  of  Buckets. — The  curve  of  bucket-spacing,  Fig.  44, 
rises  rapidly  from  zero,  where  the  buckets  are  together  and 
there  is  only  lateral  pressure,  to  8.8  pounds  for  100  pounds 
steam  pressure  and  spacing  from  |"  to  l".  The  in: pulse  then 
drops  off  gradually.  The  curve  indicates  that  the  spacing  may 
vary  from  V'  to  |"  without  affecting  the  efficiency  seriously; 
but  apparently  f "  to  |"  pitch  gives  the  greatest  efficiency.    This 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


127 


50  60  TO         80 

Absolute  Pressures 


Fig.  42. — Curves  showing  impulse  obt  -  ned  with  various  steam  pres- 
sures, using  varying  sizes  of  nozzle,  and  ^•a•ying  bucket  angles.  Upon  the 
basis  of  the.se  and  the  following  curves.  135°  buckets  were  decided  upon  for 
the  experimental  work. 


128 


STEAM-T  URBINES. 


130 


100 


«    80 


60 


50 


1  -  IJO  'Buckets  ^' 

Dia.  St.   Noz.,  Sharp  Inlet 

2-  135' 

.         M 

3-  150' 

4-  135' 

i 

4  -  15U' 

•      W 

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5-130' 
6-  135' 

a' 

•   Rounded    •■ 

"        "        ..       Sharp 

7 

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7-150' 

•  ■    M' 

•■   Expanding  Noz.,  Rounded  •> 

.<s>-^ 

8  -  135' 

%' 

•  •    St.   Noz.,   Sharp   Inlet 

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Length 

ot  Buckets,  K  Material.  Tobin  Bronze, 

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Rolled 

and  Buckets  Milled  from  Rod. 

0 


30 


100 


120 


)  50  GO  "0  80 

Absolute  Pressure. 

Fig.  43. — Impulse  on  buckets  as  produced  by  different  nozzles.  These 
curves  express  efficiency  of  buckets  and  nozzles  together,  in  terms  of  im- 
pulse per  pound  of  steam  u.sed. 


DAIA     !-i)R    CUR\'ES    OF    VELOCITY. 


,  Sharp   Extilance. 


135° 

Bu 

CKETS. 

70.5 

122S 

l.WO 

88 

1532 

1630 

98.5 

171S 

1840 

l()l> 

1845 

2000 

110  5 

1920 

2100 

111 

1982 

2170 

110, S 

2025 

2230 

lis 

2055 

2275 

118.9 

2065 

2310 

IIHT   Noz 

LE 

Sharp  K 

mtkance. 

150°  13 

OCKETS. 

OS 

1135 

1300 

83.5 

1395 

1830 

>J4 . 5 

1580 

1840 

102 

1705 

2000 

107 

1790 

2100 

111 

1855 

2170 

11.) 

1887 

2230 

115 

1920 

2275 

,HT  Nozzi 

p 

Rounded 

ExTR.vNcr 

150° 

Uu 

JKETS. 

70 

1170 

1330 

87.5 

1460 

1700 

97.2 

1620 

1900 

10.-i.7      . 

1730 

2040 

108.5 

1810 

2150 

112  2 

1875 

2230 

114.2 

1910 

2280 

116 

1940 

2320 

RING    Noz 

LE 

Rounded 

Entranc 

150° 

Buckets. 

30 

62 

1035 

1100 

40 

77 

1285 

1460 

50 

88 

1470 

1720 

60 

97 

1620 

1940 

70 

105 

1750 

2140 

80 

112 

1870 

2290 

!K1 

lis 

1970 

2390 

100 

122 

2040 

24S0 

110 

i"  Straight  Nozzle,  Sharp  Entrance.  . . 

}"  Straight  Nozzle,  Rounded  Entrance . . .  ) 

J"  Expanding  Nozzle,  Rounded  Entrance  ] 


!  1,  Velocity  from  Reaction. 

Impulse,  on  135°  Buckets. 


'  1.50°     " 
Reaction. 

Impulse,  150°  Buckets. 
Reaction. 
Impulse,  150°  Buckets. 


Jiole. — These  curves  show  comparative  values  of  the  velocity  of  steam-jets  as  calculated  from  the  measured 
reaction  again.st  the  nozzle  and  attachments,  and  from  the  impulse  exerted  by  the  jet.-;  upon  the  buckets  shown 
in  Fig.  43.  The  los.ses  due  to  friction,  eddies,  etc..  in  the  buckets,  cause  the  velocity  a."  indicated  by  the  impulse 
to  be  less  than  that  indicated  hy  the  reaction.  Curves  6  and  7,  from  the  expanding  nozzle,  show  the  same  char- 
acteristics as  noted  at  bottom  of  page  125,  and  as  shown  also  by  Curve  7,  Fig.  43. 

{To  face  page  128. 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM. 


129 


being  a  convenient  spacing  from  constructive  considerations,  it 
was  adopted  for  the  subsequent  experiments. 

Effect  of  Clearance  between  the   Nozzle  and  the  Buckets.— 

By  means  of  shims  between  the  nozzle  support  and  the  clamp 


Impulse  at  100  pounds  gage  pressure 

O 1-' »0 CO 1^ C^ O -v» ca 13 o 


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carrying  the  buckets,  the  effect  of  placing  the  nozzle  end  at 
varying  distances  from  the  buckets  was  tested,  the  distances 
varying  from  M"  to  W •  Very  little  difference  in  impulse 
could  be  detected,  and  only  a  few  points  were  found,  as  shown 


130  STEAM-TURBINES. 

in  Fig.  45.  Apparently  within  the  limits  used,  the  distance 
of  the  nozzle  from  the  buckets  is  not  of  great  importance. 

Effect  of  Additional  Sets  of  Buckets,  through  which  the  steam 
passes  on  its  way  to  the  movable  buckets. 

With  one  set  of  stationary  nozzles  clamped  in  front  of  the 
movable  buckets  (these  being  reversed  in  position  and  the  scales 
counter-weighted  so  as  to  measure  the  impulse),  at  100  pounds 
per  square  inch  gage  pressure,  the  impulse  on  the  movable 
buckets  was  6  pounds.  With  two  stationary  sets  clamped  together 
without  clearance  between  them,  and  placed  before  the  movable 
nozzles  as  before,  the  impulse  on  the  movable  buckets  was  4.8 
lbs.  With  three  sets  of  stationary  buckets  the  impulse  was 
3.6  pounds.  When  no  extra  sets  of  buckets  were  used,  the 
impulse  on  the  movable  buckets  due  to  the  direct  jet  from  the 
nozzle  was  8.8  pounds  for  an  initial  pressure  of  100  pounds 
gage. 

If  with  two  extra  sets  the  first  set  of  extra  buckets  (station- 
ary) should  receive  8.8  pounds,  the  second  set  6,  and  the  movable 
4.8  pounds,  the  total  impulse  would  be  the  sum  of  8.8,  6.0, 
and  4.8,  or  19.6  pounds.  The  upper  curve  (Fig.  46)  was  plotted 
upon  this  assumption,  adding  to  the  impulse  of  the  first  set 
that  of  all  the  following.  It  has  been  the  experience  of  builders  of 
the  many-stage  impulse-turbine  that  the  pressure  beyond  a  row 
of  buckets  is  often  higher  than  that  before  it,  and  it  is  probable 
that  in  the  arrangement  under  discussion  the  steam-flow  would 
be  checked  by  the  accumulation  of  pressure  in  the  later  buckets, 
thus  preventing  the  full  impulse  from  being  realized. 

The  middle  curve  shows  the  obtainable  impulse  for  the 
ordinary  arrangement  of  impulse-turbine,  in  which  only  the 
alternate  rows  of  buckets  rotate,  the  others  being  the  stationary 
guides.  The  total  impulse  given  by  this  arrangement  is  much 
greater  than  that  given  by  the  single  row  of  buckets,  but  not 
as  great  as  though  all  the  rows  rotated. 

While  these  curves  indicate  relative  values  of  the  losses 
occurring  in  the  guide-blades,  the  results  are  probably  quite 
different,  numerically,  when  the  movable  buckets  are  travelling 


EXPERIMENTAL   WORK  OX  FLOW  OF  STEAM. 


131 


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Impulse  at  100  Pounds  Gage  Pressure 


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132 


STEAM-TURBINES. 


rapidJv  in  front  of  the  guide-buckets  and  disturbing  the  steady 
flow  of  steam. 

Effect  of  Clearance  between  Sets  of  Buckets. — In  turbine 
construction  it  is  necessary  to  provide  clearance  between  the 


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moving  and  stationary  rows  of  blades  or  buckets,  and  this 
was  not  allowed  in  the  previously  described  experiment  for 
finding  the  effect  upon  the  impulse  of  increasing  the  number 
of  rows  of  stationary  buckets. 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM.  133 

To  determine  the  effect  of  clearance  two  sets  of  stationary 
buckets  were  placed  before  the  movable  set,  and  the  clearance 
was  obtained  by  interposing  strips  of  sheet  metal  between 
the  stationary  sets.  Runs  were  made  with  clearances  of  i^", 
x^   ,  and  g   . 

The  curve  at  the  top  of  Fig.  47  shows  the  impulse  at  SO 
pounds  initial  pressure  with  varying  amounts  of  clearance. 
The  points  determined  all  fall  on  a  smooth  curve,  and  show  that 
clearance  up  to  h"  has  apparently  very  little  effect  in  diminish- 
ing impulse.  From  h"  to  ^"  the  loss  is  noticeable,  and  after 
^'  it  is  great,  increasing  rapidly  with  the  clearance.  On  the 
lower  part  of  the  page  are  shown  curves  of  impulse  with  differ- 
ent clearances.  Calling  the  impulse  obtained  with  no  clearance 
at  all  100  per  cent,  the  losses  due  to  increased  clearance  are  as 
follows  at  100  pds.  initial  pressure  by  gage. 

Buckets  clamped  close  together,  no 

clearance impulse  4.8  pds.  =  100% 

A-inch  clearance "■        4.8    "    =  100% 

A-  "           "       ''        4.5    ''    =  94% 

"        3.6    ''    =   75% 

These  figures  and  the  curves  indicate  that  the  clearance 
between  rows  has  an  important  bearing  upon  turbine  econ- 
omy. A  certain  amount  of  clearance  is  necessary  for  me- 
chanical reasons,  especially  since  the  parts  of  the  machine  are 
exposed  to  high  temperatures.  Especial  attention  to  this 
point  is  required  in  machines  that  are  to  use  superheated 
steam. 

Use  of  Air  instead  of  Steam. — The  nozzle  directing  the 
jet  upon  the  buckets  was  attached  to  a  source  of  compressed- 
air  supply,  the  remainder  of  the  apparatus  being  the  same 
as  that  used  in  the  steam  experiments  excepting  that  the 
canvas  shield  used  with  steam  was  no  longer  necessary. 

As  is  shown  by  the  curves  (Figs.  48  and  50),  the  impulse 
with  air  was  in  each  case  about  12  per  cent  higher  than  with 
steam  of  corresponding  initial  pressure.     The  effects  produced 


134 


STEAM-TURBINES. 


Clearance  between  Sets  of  Buckets,  Inches 

Vm  Vl6  ^'2  % 


•a    3 


100 


90 


■§80 


iOO 


,40 


30 


20 


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if 

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0        1        2        3        4        5        c 

Impulse,  Pounds 

Fig.   47. — Relation   between   impulse   and   clearance   between   buckets, 
showing  decrease  of  the  impulse  due  to  increase  of  clearance. 


EXPERIMENTAL  WORK  OX  FLOW  OF  STEAM. 


135 


were  the  same  in  character  as  those  produced  by  steam,  and  as 
air  was  more  agreeable  to  operate,  the  remaining  experiments 
were  made  with  it  instead  of  steam. 

Effect  of  "Cutting  Over"  the  Edges  of  the  Buckets. — The 
nozzle  angle  was  shifted  from  its  former  position  so  that  instead 
of  directing  the  jet  tangentially  upon  the  bucket  surfaces  at 
entrance,  it  caused  the  stream  to  be  divided  or  spht  by  the 


9 

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1  ::  o  4  5  0  7  8  9  10  11  12 

Impulse  ot  Air  Jet  on  Buckets,  Pounds 

Fig.  48. — Relation  between  impulse  produced  by  steam  and  by  air. 

edges.  The  results  are  shown  in  Fig.  49  for  100  pounds 
initial  pressure.  The  most  efficient  angle  was  found  to  be 
that  given  tangency  of  the  stream  to  the  buckets,  or  22|  degrees 
with  the  vertical.  Larger  angles  cause  an  action  against  the 
backs  of  the  buckets,  while  with  smaller  angles  the  stream 
is  spread  by  the  edges  of  a  number  of  buckets  and  does  not 
strike  any  as  efficiently  as  when  directed  tangentially  to  the 
bucket  surfaces  at  entrance. 


136 


STEA  M-TURBINES. 


Efficiency  of  Rough  Surface  Buckets  as  Compared  with  those 
having  Smooth  Surfaces. — The  buckets  as  used  in  the  previous 
experiments  had  been  finished  to  very  smooth  surfaces  and 
it  was  desired  to  find  out  to  what  extent  this  contributed 
towards  high  efficiency.  The  buckets  were  therefore  taken 
from   the   clamps,    covered   with   shellac   and   sprinkled  with 


12 

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20"^  30° 

ANGLE  OF  NOZZLE  WITH  VERTICAL 


Fig.  49. — Effect  of  cutting  over  the  edges  of  the  buckets.     For  these  ex- 
periments 22^°  was  found  to  be  the  angle  of  nozzles  giving  highest  efficiency. 

brass  filings.  These  were  allowed  to  stick  and  they  effectu- 
ally roughened  the  surfaces.  The  buckets  were  then  reset 
in  the  clamps  and  runs  were  made,  using  air  as  the  working 
fluid,  with  one  set  of  movable  buckets  and  also  with  two  sta- 
tionarv  sets  placed  before  the  movable  set. 


EXPERIMENTAL   WORK  ON   FLOW  OF   STEAM. 


137 


pi 


p  o 


p 


Impulse  on  Buckets,  Pounds 

V 

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138 


STEAM-TURBINES. 


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EXPERIMENTAL   WORK  OX  FLOW  OF  STEAM.  139 

The  losses  resulting  from  incieased  skin  friction  were  very 
considerable.  With  one  set  of  movable  buckets  only,  the 
loss  amounted  to  6  per  cent — that  is,  the  impulse  at  100  pounds 
initial  gage  pressure  was  only  94  per  cent  of  the  impulse  for 
smooth  buckets  at  the  same  pressure.  The  curves,  Fig.  51, 
show  the  relation  l^etween  the  impulse  as  received  upon  smooth 
and  upon  rough  buckets  respectively.  The  runs  made  with 
two  extra  sets  of  rough  buckets  placed  before  the  set  of  mov- 
able buckets  show  very  much  increased  losses  and  indicate 
that  the  loss  is  directly  proportional  to  the  number  of  sets 
added.  The  investigators  plotted  a  curve  (not  reproduced 
here)  based  on  this  incUcation,  and  concluded  that,  calling  the 
smooth  buckets  100  per  cent  efficient,  the  following  would 
result  from  the  addition  of  successive  sets  of  rough  buckets 
of  the  kind  employed  in  the  experiments. 

Efficiency. 

One  set  smooth  buckets 100  per  cent. 

"     "    rough        "      94    ''       " 

Two  sets  rough      "      82    "       '' 

Three  "       "  "      64    ''       " 

Four    "        "  "      42    '' 

This  means  that  if  the  working  fluid  were  caused  to  pass 
through  four  sets  of  such  rough  buckets  as  used,  before  strik- 
ing the  single  movable  row  of  rough  buckets,  the  impulse 
upon  the  latter  would  be  less  than  half  of  what  would  be  obtained 
with  one  set  of  smooth  buckets  acted  upon  directly  by  the 
jet  from  the  nozzle. 

The  fcUowing  inferences  are  drawn  from  the  experimental 
work  discussed  in  the  preceding  pages : 

1.  Rate  of  flow,  by  weight,  is  greater  through  an  orifice 
with  rounded  entrance  than  if  the  entrance  is  sharp- cornered 
or  only  shghtly  rounded. 

2.  Rate  of  flow,  by  weight,  is  decrea.^ed  by  the  addition  of 
a  nozzle,  either  diverging  or  straight,  to  the  discharge  side  of 
the  orifice. 


140  STEAM-TURBINES. 

3.  Rate  of  flow,  by  weight,  reaches  a  maximum  when  the 
final  pressure  is  from  about  0.85  to  0.50  times  the  absolute 
initial  pressure. 

4.  The  maximum  rate  of  flow  from  the  sharp- cornered 
orifice  occurs  after  a  somewhat  greater  reduction  of  back  pres- 

Q 


P_E 


Apparatus  used  by  Mr.  George  Wilson,  for  determining  reaction  due  to  steam 
flow  from  orifice  at  M.    (Reproduced  from  London  "Engineering,"  1872.) 

sure  than  is  required  with  the  rounded  orifice  to  bring  about 
the  maximum  rate  of  flow. 

5.  The  addition  of  a  divergent  nozzle  to  the  orifice  seems 
to  cause  the  maximum  rate  of  flow  to  occur  earUer — that  is, 
after  less  reduction  of  back  pressure — than  is  the  case  with  the 
simple  orifice. 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM.  141 

6.  The  velocity  attained  depends  to  some  extent  upon  the 
rounding  of  the  orifice  or  entrance  to  the  nozzle,  and  may  be 
greater  with  the  st^uare  or  shghtly  rounded  entrance  than 
when  the  rounding  is  of  greater  radius. 

7.  As  shown  in  Figs.  53  and  54,  from  the  experiments 
of   Messrs.  Weber   and    Law   in   Sibley  College,  and   Fig.   55, 


Apparatus  used  in  Sibley  College  experiments  with  nozzles  and  buckets. 

from  Dr.  Stodola's  "Steam-turbines,"  there  is,  with  all  shapes 
of  orifice  there  represented,  a  sudden  drop  of  pressure  imme- 
diately in  the  narrowest  section  of  the  orifice,  to  below  the 
back  pressure,  then  a  rise  of  pressure  as  the  steam  leaves 
the  .orifice,  accompanied  by  variations  above  and  below  the 
back  pressure,  till  the  pressure  in  the  jet  gradually  steadies 
down  to  that  of  the  medium  into  which  it  is  flowing.  The 
Sibley  College  experiments  were  made  with  the  searching-tube 


142 


STEAM-TURBINES. 


120     110      100      00       so 


ro  ''KGO         50  40  30         20  10  0 

P,=  05.30   Vn" 


Fig.  52. — Curves  representing  ideal  conditions  of  flow,  with  adiabatic 
expansion,  and  nozzle  cross-sections  made  so  as  to  carry  out  such  expan- 
sion 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


143 


communicating  Vvith  the  piston  of  an  ordinary  steam-engine 
indicator,  and  the  rapid  vibrations  were  not  indicated  to  the 
same  extent  as  in  the  experiments  described  by  Dr.  Stodola. 


Effect  of  Increased  Back  Pressure. 


120 


100 


20 


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,-Theoi 

•etical 

1 

^-'^'^^ 

1 

• 

— 

u 

I 

Throat  Line 

y 

^ 

r 

D  .. 

\ 

=  .585 

/ 

/ 

/ 

^ 

""^ 

c 
a 
o 
p. 

/ 

/ 

/ 

a 

to 

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( 

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V 

A.tm. 

'        . 

/ 

S 

Inc 

hes. 

00  — ; 


40 


120 


lOO 


80 


60 


40 


20 


Fig.  53. — Nozzle  used  in  experiments  of  Messrs.  Weber  and  Law,  and  curves 
obtained  with  varying  back  pressiu-es. 

8.  According  to  the  experimental  work  discussed,  a  simple 
orifice  is  more  efficient  than  an  expanding  nozzle  for  initial 


144 


STEAM-TURBINES. 


pressure  up  to  about  70  pounds  absolute;  for  higher  initial 
pressures  an  expanding  nozzle,  with  entrance  only  slightly 
rounded,  is  to  be  used,  and  its  efficiency  increases  as  the  initial 


1 

L      1       1 

EFFECT  OF  BACK  FjRESJ 

URE 

-  , 

Al 

1  absci 

ssae  a 

re  trip 

led. 

> 

<'//•--//// 

100 

\ 

«0 

I 

A 

V 

V 

i 

B 

1 

V 

b 

^\ 

/ 

C 

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H 

20 

\ 

V 

/ 

'Atm. 

\, 

\ 
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D 

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'^ 

0 

"v. 

^- 

^ 

0.5 


Inches 


1.0 


100 


80. 


a 
60 1 


40  S 


20 


Fig.  54. — Orifice  used  by  Messrs.  Weber  and  Law,  and  curves  obtained  with 
varying  back  pressures. 


pressure  increases.  Plate  III  shows  a  value  of  ?/  =  0.06  for 
pressures  about  200  pounds  by  gage.  Such  high  efficiency 
cannot  be  obtained  with  an  incorrectly  designed  nozzle. 

9.  It  appears  that  steam  flowing  through  a  simple  orifice 
does  not  attain  a  greater  velocity,  while  in  the  orifice  itself,  than 
from  1400  to  1500  feet  per  second,  no  matter  how  much  the 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


145 


pressure  is  reduced  in  the  receiving  space.  However,  as  shown 
on  page  117,  the  velocity  of  the  jot  issuing  from  a  simple 
orifice  into  the  atmosphere,  as  inchoated  by  the  reaction 
against  the  discharging  vessel,  may  be  as  high  as  from  2000 
to  2700  feet  per  second.    The  fact   that   the  weight  of  flow 


i     'A      1     M 

1 



^ 

= 

c 

-- 

— 

- 

f 

D 

■^ 

•^ 

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160  15O14013ul-Ol!UliH)  90  SO    70   60   50  W   30  20  10    0  -10-20 

-: ^  Nozzle  Ajtis  »iim 

Fig.  55.* 

can  be  so  closely  calculated  upon  the  basis  of  a  heat  drop  cor- 
responding to  about  1500  feet  per  second  velocity  in  the  orifice 
is  significant  of  the  truth  of  the  first  statement.  The  additional 
circumstances  that  the  reaction  indicates  a  much  greater  final 
velocity  of  efflux,  and  that  the  simple  orifice  has  been  found  in 
practice  to  be  superior  in  efficiency  to  the  expanding  nozzle 


*  Figs.  55,  55(7,  and  56  are  from  Dr.  Stodola's  book  on  Steam  Turbines. 


146  STEAM-TURBINES. 

for  low  initial  pressures,  lead  to  the  conclusion  that  a  consid- 
erable portion  of  the  energy  in  the  steam  after  it  leaves  the 
throat  is  effective  in  further  accelerating  the  jet  in  its  initial 
direction.  The  remainder  of  the  energy  given  up  is  spent 
in  producing  the  vibrations  already  described,  and  in  causing 
a  general  displacement  of  the  atmosphere  into  wliich  the  jet 
flows.  It  is  the  province  of  the  expanding  nozzle  attached 
to  the  simple  orifice  to  contain  the  steam  during  its  total 
expansion  from  initial  to  lowest  possible  back  pressure,  and 
to  thus  cause  the  velocity  of  the  jet  to  attain  the  maximum 
value  corresponding  to  the  total  change  from  energy  in  the 
form  of  heat  to  kinetic  energy  of  the  jet,  and  to  direct  the  flow 
into  a  given  line  of  action,  so  that  the  jet  may  be  usefully 
employed. 

10.  In  the  divergent  or  expanding  nozzle  the  interchange 
of  heat  energy  between  the  steam  and  the  walls  of  the  nozzle 
causes  more  heat  to  be  rejected  in  the  exliaust  than  would  be 
rejected  if  the  flow  were  frictionless.  This  is  one  cause  of  loss 
of  energy  and  therefore  of  diminished  efficiency. 

11.  Another  loss  of  energy  may  occur,  due  to  incorrect 
proportions  of  the  nozzle;  that  is,  while  having  correct  cross- 
sectional  areas  for  the  desired  flow  of  steam,  the  nozzle  may 
be  too  long  or  too  short,  and  thus  the  angle  of  divergence  may 
be  such  that  the  jet  will  leave  the  nozzle  walls  and  so  not  fill 
out  the  cross-sections.  This  leads  to  vibrations  of  the  stream 
and  consequent  loss  of  energy.  The  nozzle  should  be  so  ar- 
ranged that  the  steam  will  expand  while  in  the  nozzle  to  just 
the  pressure  of  the  medium  into  which  it  is  to  flow.  The  curves 
A,  C,  and  D,  in  Fig.  56,  show  the  vibrations  occurring  when 
the  back  pressure  is  either  less  or  greater  than  that  at  the  end 
of  expansion  in  the  nozzle.  Curve  B  shows  the  correct  con- 
dition, the  back  pressure  being  just  that  at  the  large  end  of 
the  nozzle.  In  Figs.  53  and  54  are  shown  curves  obtained  by 
Messrs.  Weber  and  Law  by  the  use  of  a  searching-tube  and 
indicator  as  before  described. 

These  curves   show,  for  varying   back  pressures  but  con- 


EXPERIMENTAL  WORK  ON  FLOW  OF  STEAM. 


147 


stant  initial  pressure,  the  drop  occurring  at  once  upon  arrival 
of  the  steam  in  the  throat  of  the  nozzle,  and  the  rise  following 
the   initial    drop   of   pressure.    The   smooth    curve   bounding 


Itj/qpm 

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I'J   1«    IT    10    10    H    13   12    11   10      cm  20   19   13    17   16   15   H    IJ   13    11  10 


I-J.05 

r  ' 


Fig.  tba. 


cm  20  .19   18  n    16   15   H   13   12   11  IS 
12.10 


the  ends  of  the  pressure  curves  on  Fig.  55  is  the  curve  of 
adiabatic  expansion. 

The  fact  seems  to  be  that  a  great  increase  in  velocitj'^  occurs 
at  entrance  to  the  nozzle,  after  which  the  velocity  is  checked 
and  the  pressure  rises.     Dr.  Stodola  explains  this  as  "...  be- 


148 


5  TEA  M-  T  URBINES . 


cause  steam  particles  possessed  of  great  velocity  strike  against 
a  slower-mo\dng  steam  mass,  and  are  therefore  compressed  to 
a  higher  degree  .  .  .  according  to  the  theory  of  'compression 
shock '  of  Von  Riemann." 

Curve  N,  Plate  IX,  was  plotted  from  a  tabulated  series 
of  results  of  experiments  pubhshed  by  Dr.  Stodola  in  his  work, 
"The  Steam-turbine."  The  curve  represents  the  fall  in  pres- 
sure as  the  steam  advanced  along  the  nozzle  shown  above  the 
curves;   curve  A  has  been  calculated  with  the  value  y  =  0.20. 


kglqcm 

1,6 

(\^ 

k  /v 

D 

1,4 

1,5 

Sl,0 

/ 

r\ 

V 

/ 

f 

[/ 

X 

/" 

^ 



C 

^ 

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\J 

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nd 

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v>/'rr7z>. 

^Nozzle  t 

V 

-30 


-•^0     -10 


10        iJO        30        40        50 
Distance  along  Nozzle 


00 


70       80 
mm 


Fig.  56. 


This  is  seen  to  coincide  very  closely  mth  the  experimentally 
determined  curve. 

Curves  B  and  C  represent  calculated  pressures  along  the 
nozzle  wdth  allowances  of  10%  and  0  energy  loss  respect- 
ively. Assuming  that  the  nozzle  was  so  designed  that  the 
steam  filled  out  the  cross-sectional  areas,  the  velocities  along 
the  nozzle  were  as  given  by  the  velocity  curve,  reaching  about 
3400  feet  per  second. 

The  experimentally  determined  pressures  used  in  plotting 
curve  N  were  those  obtained  with  the  hole  in  the  side  of  the 
searching-tube  sloping   against    the   stream,  and    were   higher 


EXPERIMENTAL   WORK  ON  FLOW  OF  STEAM. 


U9 


PLATE  IX. 


2  3  4  5  6 

Distauce  along  nozzle, —  inches. 


150  STEAM-TURBINES. 

than  when  the  hole  was  normal,  or  when  it  sloped  away  from 
the  stream.  If  the  lower  values  are  more  nearly  correct,  then 
the  energy  loss  was  less  than  20%. 

The  initial  pressm'e  used  in  the  experiments  is  given  as 
149  pounds  absolute.  By  comparing  the  friction  loss  of  20% 
with  that  indicated  on  Plate  III,  the  latter  is,  for  the  same 
initial  pressure,  only  12%,  and  tliis  tends  to  confirm  the 
inference  pointed  out  by  Dr.  Stodola,  that  the  friction  loss 
is  lower  than  20%.  The  values  of  y  calculated  in  the  lable 
at  the  end  of  Chapter  V,  from  the  Sibley  College  experiments, 
show,  for  110  pounds  absolute  pressure,  a  frictional  loss  of 
12.5%  in  the  expanding  nozzle  used. 


CHAPTER  VII. 

THE     IMPULSE-TIRBIXE. 

The  impulse-turbine  may  be  designed  in  any  one  of  the 
following  waj's: 

(a)  Single  stage,  consisting  of  a  set  of  nozzles  and  a  single 
wheel  carrying  one  row  of  blades.  The  pressure  is  the  same 
on  the  two  sides  of  the  wheel,  or  disc,  the  whole  pressure  drop 
occurring  in  the  nozzles.  This  gives  very  high  peripheral 
velocity,  and  since  the  cUameter  must  be  kept  small  enough 
to  keep  frictional  resistances  within  Hmits,  the  number  of 
revolutions  is  very  great.  The  de  Laval  turbines  run  at  speeds 
of  from  10,000  to  30,000  revolutions  per  minute,  gi^'ing  a 
peripheral  velocity  of  1200  to  1400  ft.  per  second.  The  exces- 
sive angular  velocity  of  the  rotating  part  necessitates  the  use 
of  gearing  in  apph'ing  the  power  to  machines. 

(6)  Other  rows  of  blades  may  be  added,  either  upon  the 
single  wheel  or  upon  separate  wheels,  in  order  more  com- 
pletely to  absorb  the  energy  of  the  steam  leaving  the  nozzles. 
There  is  no  further  pressure  drop,  however,  after  leaving  the 
nozzles,  and  only  one  set  of  the  latter  is  supplied.  This  type 
has  therefore  a  single  pressure  stage  and  several  velocity 
stages. 

(c)  The  first  nozzles  may  be  so  arranged  as  to  expand  the 
steam  through  onl}^  a  portion  of  the  pressure  and  temperature 
range  available,  thus  causing  the  steam  to  leave  the  first  set 
of  nozzles  at  a  much  lower  velocity  than  results  from  the  single- 

151 


152  STEAM-TURBINES. 

pressure-stage  turbine.  Since  good  efficiency  demands  that 
the  peripheral  velocity  of  the  blades  be  proportional  to  the 
entering  steam  velocity,  the  peripheral  velocity  may  be  decreased 
with  the  decrease  of  steam  velocity.  The  steam  is  reduced  in 
the  first  nozzles  to  a  pressure  considerably  higher  than  the 
condenser  pressure,  and  hence  may  be  expanded  through 
another  set  of  nozzles  arranged  to  discharge  upon  another  set 
of  blades,  on  a  separate  wheel,  in  a  separate  compartment  or 
division  of  the  turbine-casing  from  that  containing  the  first 
wheel.  The  second  set  of  nozzles  and  blades  constitutes  the 
second  stage  of  the  turbine.  By  sufficiently  hmiting  the 
pressure  drop  that  can  occur  in  a  single  set  of  nozzles,  the 
velocity  of  exit  of  the  steam,  and  consequently  the  necessary 
peripheral  velocity  of  the  blades,  may  be  greatly  reduced. 
The  many-stage  impulse-turbine  thus  consists  of  several 
single-stage  turbines,  placed  in  series  with  one  another.  The 
steam  leaves  each  set  of  blades  with  considerable  velocity, 
but  since  the  next  wheel  is  in  a  separate  chamber,  and  the 
steam  has  to  pass  through  a  set  of  orifices  or  nozzles  to  reach 
it,  the  exit  velocity  cannot  be  used  as  velocity.  The  steam 
comes  partially  to  rest  before  going  through  the  next  nozzles, 
and  the  energy  in  the  exhaust  from  the  preceding  blades  is 
expended  in  producing  impact,  and  consequently  in  raising 
the  temperature  and  pressure  of  the  steam  before  it  enters 
the  succeeding  nozzles.  Thus  the  exit  velocity  from  all  but 
the  wheel  next  to  the  condenser  is  effective  in  doing  work  in 
the  turbine.  In  passing  through  the  chambers  and  passages 
there  is  loss  due  to  leakage  through  the  clearance  spaces,  and 
this  causes  loss  of  the  heat  in  a  certain  amount  of  steam  which 
gets  through  \\dthout  doing  work  on  the  turbine-buckets. 

The  Single-stage  Impulse-turbine. — The  velocity  of  steam  at 
exit  from  a  nozzle  may  be  determined  as  previously  indicated, 
and  gives  the  value  shown  by  V  in  Fig.  57,  being  the  abso- 
lute velocity  of  the  steam  as  it  enters  the  turbine. 

Considering  first  a  simple  impulse-wheel,  rotating  ■^ith  a 
peripheral  velocity  of  n  feet  per  second,  the  velocity  of  the 


THE  IMPULSE-TURBINE.  153 

entering  steam,  relatively  to  the  velocity  of  the  rotating  blades 
on  the  wheel,  will  be  represented  by  v  {=AC)  in  magnitude  and 
direction.  In  order  that  the  steam  may  enter  the  blades 
without  shock,  the  angle  of  the  entering  edge  of  the  blades 
with  the  direction  of  motion,  u,  must  be  J,  the  same  as  the  direc- 
tion of  relative  velocity  of  the  entering  steam.  Assuming  that 
no  frictional  losses  occur  in  the  blade-channels,  the  relative 
exit  velocity  will  be  Vi  =  i'.  The  angle  of  exit  may  be  marie 
according  to  the  judgment  of  the  designer,  and,  as  has  been 


Fig.  57. 

seen  (see  page  20),  this  angle  determines  to  a  great  extent 
the  efficiency  of  the  wheel.  Mechanical  considerations  prevent 
the  obtaining  of  complete  reversal  of  the  jet  in  this  type  of 
turbine.  Usually  the  angle  ^3  is  made  equal  to  the  angle  J, 
and  the  cross-sectional  area  at  exit  from  the  blades  equals 
that  at  entrance  to  them. 

It  is  shown  by  the  examples  on  page  23  that  if  V  and 
Vi  are,  respectively,  the  absolute  velocities  of  the  entering 
and  departing  steam,  the  work  done  upon  the  blades  by  W 
pounds  of  steam  passing  them  per  second  is 

K --=  W(V2-  Fi2)  ^ 2g,  foot-pounds. 


154  STEAM-TURBINES 

2g 


TFF2 

Since  the  kinetic  energy  at  velocity  7=-^—,  the  efficiency 


F2-Fi2 

IS         y2       • 

The  velocities  may  be  represented  as  shown  in  Fig.  58,  V 
and  Vi  being  the  initial  and  final  absolute  velocities  respect- 
ively. 

Let  the  initial  velocity  be  3500  feet  per  second,  =  V. 

"    a -30°. 

''  peripheral  velocity  =  1200  feet  per  second,  =u.  For 
the  ideal  case  shown  at  the  left  on  Plate  X  the  relative  entrance 
and  exit  velocity  is  i'  =  2540  ft.  per  sec.  This  gives  T^,  the 
absolute  exit  velocity,  as  1870  ft.  per  sec.  The  energy  given 
up  to  the  buckets,  per  pound  of  steam,  is 

(^^00';;f'°'^  136,000  foot-pounds.     ^ 

This  may  also  be  computed  by  resolving  the  absolute  veloci- 
ties V  and  Vi  along  the  direction  of  motion  of  the  buckets, 
and  adding  the  components,  multiplying  by  the  peripheral 
velocity,  u,  and  dividing  by  g.  The  horizontal  components 
may  be  taken  from  the  diagram  by  measurement. 

Thus  the  energy  given  up  is 

{C^Qu    (3030  + 640)  X 1200     .....^^ 
-g = 32:2 =  ^^^'^^^  ^ ' 

Losses  in  Nozzles  and  Buckets. — As  the  steam  expands  in  the 
nozzle  it  experiences  frictional  resistances  which  cause  it  to  give 
up  less  energy  than  it  would  under  ideal  conditions  of  flow,  and 
the  loss  therefrom  diminishes  the  nozzle  exit  velocity,  F,  to  some 
value  fV  {  =  V'),  where  /  is  equal  to  the  square  root  of  the 
quantity  \  —  ym  the  example  on  page  83.  Thus,  for  2/ =  0.15, 
/-v'a85  =  0.92. 

The  coefficient  /  varies  according  to  the  length   and  other 


THE  IMPULSE-TURBINE. 


155 


156  STEAM-TURBINES. 

proportions  of  the  nozzle.  The  initial  velocity  being  V  (  =  /F) 
gives  v'  as  the  real  relative  velocity  of  the  steam  at  entrance 
to  the  first  mo\dng  blades  of  a  stage.  This  is  further  decreased, 
by  resistances  in  the  blades,  to  the  value  Vi'  =  kv'.  The  loss 
of  energy,  per  pound  of  steam,  will  be,  in  the  nozzle, 


Ln  = 

72 

2j 

72 

_  7'  2 

2j 

The 

remaining 

energy  is 

2r 

72 

—  y'2 

7^2 

2^ 

2j 

A  Une  representing  V  may  be  drawn  in  the  velocity  diagram 
at  the  right  of  Plate  X,  and  this  combined  with  u  gives  v', 
the  real  relative  velocity  at  entrance  to  the  mo\dng  blades. 
The  loss  in  the  moving  blades  is 


where  k^\/l-y',  y'  being  the  per  cent  loss  of  energy  occa- 
sioned as  the  steam  passes  through  the  moving  blades.  More 
properly,  y'  is  the  percentage  of  the  available  energy  which 
is  effective  in  heating  the  buckets  and  other  steam-passages, 
and  so  not  effective,  at  the  point  under  consideration,  for  pro- 
ducing velocity  of  flow.  The  remaining  energy,  after  deducting 
both  losses,  is 

T^'2  7/2     7/2 

p-^2_7^/2_(l_^.2)^/2 

These  quantities  are  to  be  used  in  the  modified  velocity 
diagram  at  the  right  on  Plate  X,  and  this  may  now  be  diawn 
accorcUng  to  the  following  assumptions.     Let  the  loss  tlue  to 


THE  IMPULSE-TURBINE.  157 

friction  m  the  nozzles  correspond  to  a  value  of  ?/  =  0.12:  and 
in  the  buckets  let  ?/'  =  0.14.  The  fraction  by  which  the  entrance 
velocity  is  decreased  is  /,  and  the  actual  velocity  of  the  steam 
from  the  nozzles  will  be 


y'  =  jV  =  VVl-y. 


Therefore  /=\/l-?/,  as  before  stated;  and  in  the  present 
example  the  value  is  \/0.88,  or  0.94,  approximately.  Then 
F'  =  0.94X3500  =  3290  ft.  per  second.  The  resulting  relative 
velocity  is  v'  =  2330,  and  this  is  diminished  in  the  buckets  to  a 
value  kv',  where  /v  =v'l -0.14  =  0.92S.  The  value  of  r/  is 
then  0.928x2330  =  2160  ft.  per  second,  and  the  absolute  velocity 
of  exit  from  the  buckets  is  F/  =  lo70.  The  nozzle  angle 
of  course  remains  as  it  was  before,  but  the  angle  A'  has  become 
slightly  greater  than  the  corresponding  angle  A  in  the  ideal 
case.     Tlie  work  done,  per  pound  of  steam,  is 

,„     32902 -15702- 0.14  X(  2330)2 

K'  = ~~644 ^  119,000  foot-pounds. 

The  work  done  in  the  frictionless  turbine  was  found  to  be 

^,    35002-18702     ,__^, 

A  = TTTT =  136,000  foot-pounds. 

The  efficiency  in  this  ideal  case  was 

35002-18702    ^^_ 
-    35002        =0..14. 

The  efficiency  after  deducting  the  loss  due  to  friction  is 
119,000. 


136,000 


X  0.714  =  0.624. 


This  figure  does  not  rci:)rcsent  the  true  efficiency,  because  losses 
due  to  -svindage  and  to  friction  of  journals  and  stuffing-boxes 


158  STEAM-TURBINES. 

have  not  been  considered.      Assuming  a  loss  of  10  per  cent 
due  to  these  causes,  the  work  dehvered  by  the  machine  is 

0.9  X  119,000  =  108,000  foot-pounds. 

The  efficiency  is  therefore  0.566. 

Since  one  pound  of  steam,  in  passing  through  the  turbine, 
causes  108,000  foot-pounds  of  work  to  be  dehvered  to  the  shaft, 
the  steam  consumption  of  the  machine  in  pounds  per  dehvered 
horse-power  hour  is 

1,980,000 
108,000  ■ 

Assuming  the  revolutions  of  the  wheel  per  minute  to  be 
15,000,  the  cUameter  to  give  a  peripheral  velocity  of  1200  feet 
per  second  is 

=  1.53  feet,  or  about  18|  inches. 


15,000X3.14 


If  the  wheel  were  to  deliver  100  horse-power,  it  would  use 
1840  pounds  of  steam  per  hour,  or  about  0.51  pound  per  second. 
The  nozzle  discussed  in  the  example  on  page  85  would  deliver 
about  half  of  that  amount  of  steam,  but  five  or  six  nozzles  cf 
smaller  diameter  and  length  might  better  be  used  than  two  of 
those  referred  to. 

The  dimensions  of  the  nozzles  may  be  found  by  the  same 
method  as  used  in  the  previous  nozzle  calculations. 

The  Two-stage  Impulse-turbine,  with  Several  Rows  of 
Buckets  in  Each  Stage.  —  Let  an  impulse-turbine  have  two 
stages,  each  containing  one  set  of  nozzles,  and  three  rotating 
and  two  stationary  sets  of  buckets,  as  shown  in  Fig.  60.  Let 
the  initial  pressure  at  the  throttle-valve  be  160  pounds  per 
square  inch  absolute. 

Let  expansion  in  the  first  nozzles  be  from  160  pds.  to  14 
pds.  absolute. 


THE  IMPULSE-TURBINE. 


159 


[1_M 


Fig.  60.— Vertical  section,  two-stage  Curtis  turbine,  500  K.W.,  ISOO  R.PM 


160  STEAM-TURBINES. 

Let  expansion  in  the  second  nozzles  be  from  14  pds.  to 
a  vacuum  of  29  inches  of  mercury. 

The  ideal  case  will  be  considered  first,  allowing  for  no 
losses  excepting  that  due  to  the  energy  in  the  exliaust-steam. 

From  the  curves  on  Plate  XI  it  is  found  that  the  steam 
during  its  expansion  in  the  first-stage  nozzles  gains  a  velocity 
of  2990  feet  per  second.  This  may  be  found  with  the  aid  of 
the  heat  diagram  at  the  back  of  the  book.     Thus, 

Ti ,  corresponding  to  160  pds.  absolute,  =  824°  F.  abs. 
T2,  "  "     14    "  ''        =670°  F.    " 

Assuming  100%  dry  steam, — from  the  chart,  the  total  heat 
is  1192  B.T.U.  per  pound  at  the  initial  pressure.  After  adia- 
batic  expansion  the  heat  in  the  mixture  is  1014  B.T.U 

1192-1014  =  178  B.T.U.  given  up. 

The  velocity=  F = 224 \/ 178  =  2990  ft.  per  second,  approximately. 
Let  the  peripheral  velocity  u  be  400  feet  per  second.    This 

u 
gives  a  ratio  of  tf  =  0.135. 

Let  the  angle  of  the  nozzles  "with  the  plane  of  rotation  of 
the  buckets  be  20°. 

The  velocity  diagram  for  the  first  movable  buckets  may 
be  drawn  as  before,  the  entrance  and  exit  angles  of  the 
buckets  being  the  same  as  those  made  by  the  relative  velocity 
Hues  with  the  direction  of  motion  of  the  buckets. 

From  the  relative  exit  velocity  Vi  (  =  v)  may  be  found 
the  absolute  velocity  T^,  and,  since  the  stationary  buckets 
receive  the  jet  in  the  direction  corresponding  to  the  absolute 
velocity,  they  may  be  sketched  in,  as  at  B.  These  stationary 
buckets  act  as  nozzles  for  the  succeeding  movable  buckets, 
and  the  direction  of  the  relative  velocity  line,  ?'2,  is  used  for 
determining  the  angles  of  entrance  and  exit  for  the  movable 
buckets  at  C  In  similar  manner  each  stationary  and  mov- 
able set  may  be  outlined. 


12 


:;3 


...o'.;- 

. .,  O 


'(4 

o 


-1.2  O 


CURVES 

OF 

VELOCITY  AND  DISCHARGE  OF  STEAM 

AS  COMPUTED 


'H^^HlTl+wTHSfErT^ 


TpWE^fPEF 


INITIAL  PRESSURE  FOUXlJS  PER  s"q.  IN.  AliS 

JSOTE:     FIGURES  AT  ENDS  OF  CURVES  DEN0TJ2  FINAL 
PEESSURKS  IN  INCHES  MERCURY  OR  POUNDS  ABS. 


[To  /(ice  p.  leO. 


IIZ   JTAa'i 


t£ 


^^"«  y^.-iCkiS. 


The  entrance  and  exit  angles  of  the  buckets, 
whether  moving  or  stationary,  arc  not  i 
8arily  made    equal  to  each  other,   but  are 
modified  to  suit  the  energy  distribution  aimed 
TWO  STAGE  IMPULSE  TURBINE.  at  iu  any  given  case. 


[To  face  p.  161. 


THE  IMPULSE-TURBINE.  161 

The  efficiency  of  the  system  is 

72     » 

where  Vn  is  the  final  absolute  exit  velocity.  In  the  present 
case  there  are  five  sets  of  buckets,  including  movable  and 
stationary,   and  hence  n  =  5. 

The  distance  YZ,  Plate  XII,  equals  u(n  +  l),  and 

F„2  =  F2+|(^  +  l)^,|2_2F(n  +  l)ucosa:. 

For  the  ideal  case  under  consideration  the  efficiency  is 

72 -TV     2(>i  +  l)ucosa     \(n  +  l)u\2 
F2      -  V  ~        F2       • 

In  the  single-stage  turbine  n  =  l  and  the  efficiency  is 

Y\cosa—yJ, 

as  was  shown  on  page  23,  Chapter  I. 

In  the  present  case  n  =  o;   cos  20°  =  0.94,  approx. 

2X6X400X0.94     (6)2 x  (400)2 
Efficiency  = ^990 (2990F~  ^  ^'^^  '^' 

From  the  diagram,  Plate  XII,  T^5  =  1080  ft.  per  sec. 

^^  .            (2990)2 -(1080)2 
Efficiency  = [2990)2 ^         ^ ' 

The  variation  of  efficiency  with  a  and  with  71  and  ff  is 
shown  on  plate  XVII. 

The  velocity  diagram  shown  at  the  left  on  Plate  XII  is 
for  the  ideal  case.  The  velocities  represented  by  the  various 
lines  are  as  follows: 


162  STEAM-TURBINES. 

V  =  absolute  velocity  leaving  nozzles. 
Fi=      "  "  "         buckets  No.  1. 

V2-      "  "  ''  "         "    2  and  equals  7i. 

73=      "  "  "  "         "    3. 

•r/-_        II  It  ((  (I  (t^tc  tt       Y 

75=      "  '  "  "         ''    5. 

i;  =  relative  velocity  leaving  nozzles. 
Vi=      "  "  "        buckets  No.  1  and  equals  u. 

V2=       "  "  "  "         "     2. 

V3=       "  "  "  "         "     3     "  "      V2. 

V4=      "  "  "  "        "    4. 

^5  =  O  V4,. 

Since  there  are  no  losses  during  the  passage  of  the  steam 
through  the  nozzles  and  buckets,  all  the  energy  given  up  is 
effective  in  producing  rotation,  and  the  work  done  may  be 
calculated  as  follows : 


In  first  movable  buckets,  (2990)2  -  (2230)2 
"second"  "        (2230)2- (1560)2 

"third      "  "        (1560)2 -(1080)2 


64.4  =  61,700  ft.-lbs. 
64.4  =  39,500      " 
64.4  =  19,600      " 


Total 120,800  ft.-lbs. 

This  is  to  be  compared  with  V^  —  V^  -^2g 

(2990)2 -(1080)2 


64.4 


=  120,800. 


TV.      ffi  •  •    (2990)2 -(1080)2 

The  efnciency  is ^ 0000^2 ^  ^-^ '  • 

The  velocities  obtained  in  actual  turbines  are  less  than 
those  just  considered,  because  of  the  frictional  resistances 
encountered  by  the  steam  in  its  passage  through  nozzles  and 
buckets.    The   diagram  is   therefore   to   be   modified   accord- 


THE  IMPULSE-TURBINE. 


163 


r 

1 

First  stage. 

1 — 



Movable 

Stationary 

Movable 

Stationary 

Movable 

)d. 


Second  stage. 
Curtis  turbine  buckets. 


•164  STEAM-TURBINES. 

ing  to  the  reduction  in  velocity,  and  the  blade  angles  made 
to  correspond. 

Calling  the  loss  of  energy  y,  as  before,  let  the  initial  veloc- 
ity V  correspond  to  the  value  y  =  0.08. 

The  steam,  as  it  issues  from  the  nozzle,  will  then  have  a 
velocity  of 


F'  =  224^178X0.92  =  2870  feet  per  second. 

Let  the  steam,  as  it  passes  through  the  buckets,  fail  to 
gain  the  full  velocity  of  the  ideal  case  because  of  frictional 
resistances  represented  by  the  following  values  of  y: 

During  passage  through  set  No.  1 y  =  0.03 

"     "    2 y  =  0.05 

"  "  ''         "     "    3 y  =  Om 

"  "  "         "     "    4 y  =  0.07 

"  ''  "         "     "    5 y  =  0.07 

The  velocities  to  be  used  in  laying  down  the  diagram  will 
then  be: 

V  =  2870  feet  per  second,  as  already  found. 

vi'  =  2500\/l-0.03  =  2450  feet  per  second. 

y2'  =  2080v/l-0.05  =2030    "      " 

r3'  =  1690\/l-0.06  =1640    ''      " 

7/ =  1320^/1 -0.07  =1280    "      " 


i;5'  =  1020Vl-1.07  =  985    "      " 

y5'  =  finalabsolute  velocity  =  850    "      '' 

The  resulting  modified  velocity  diagram  is  shown  in  the 
center  of  Plate  XII.  The  efficiency  of  this  stage  of  the  tur- 
bine is  not  represented,  as  before,  by  the  difference  of  the 
squares  of  the  two  absolute  velocities, — initial  and  final,  re- 
spectively,— for  the  decrease  of  the  final  velocity  V5  below  the 
value  in  the  ideal  case  is  due  to  the  fact  that  the  steam  is 
carrying  away  with  it  heat  energy,  which  in  the  ideal  case 


THE  IMPULSE-TURBINE.  165 

would  1)0  given  up  as  kinetic  energy  corresponding  to  in- 
creased velocity.  The  heat  carried  away  is  available  for  doing 
work  in  the  second  stage  of  the  turbine. 

The  work  done  on  each  of  the  movable  sets  of  buckets 
may  be  determined  as  was  done  in  the  case  of  the  single-stage 
turbine  discussed  on  page  157.  Thus,  for  the  nozzles  and 
first  moving  buckets, 


V'  =  jV,     where     /=\/l-i/=\/l -0.08  =  0.96. 
Therefore      F'  =  0.96x2990  =  2870  feet  per  second. 
The  work  done  on  the  first  moving  buckets  is 

K,'  =  1  {V'Y  -  (F/)2  -  (1  -k^y  2 1  -2f/ 

28702  -  20802  -  0.03  X  25002     _  ^^^  , 
= g^l =58,000  ft.-pds. 

Similarly,  the  work  done  on  the  second  moving  buckets,  that  is, 
on  set  No.  3,  is 

IW  =  !  (F/)^ -  {V^y  -  (1  - yl-32)i'o'2 1  ^2g 

20302  - 13302  -  0.06  X 16902     ^^  ^^^  , 
=  — — ^^ =  33,800  ft.-pds. 

Finally,  the  work  done  on  the  last  moving  buckets  (set  No. 
5)  is  " 

12802  -  8502  -  0.07  X 10302     _  _^  , 

= 64:4 ^  ^^'^^^  ^^•■p'^'- 

The  total  work  done  on  the  w'heels  by  the  steam,  per  pound, 
is  the  sum  of  these  amounts,  or  104,900  foot-pounds. 

In  the  ideal  case  the  work  was  120,800  foot-pounds,  and 
the  efficiency  was  0.87. 


166  S  TEA  M-  T  UR  BINES. 

The  efficiency  in  the  present  case  is 

104,900. 


120,800 


X  0.87  =  0.755. 


The  steam  consumption  of  this  turbine,  if  no  further  stage 
were  added,  would  be 

1.980,000     .00  1  1.  1. 

^^,  ^„„  =  18.9  pounds  per  horse-power  hour. 
104,900  ^  '■  ^ 

If  there  were  a  loss  of  10%,  due  to  friction  of  journals  and 
to  windage,  as  was  assumed  in  the  case  of  the  simple  impulse- 
turbine  of  one  rotating  wheel,  the  steam  consumption  of  the 
first  stage  of  turbine  in  the  present  example,  if  worked  alone, 
would  be  about  21  pounds  per  horse-power  hour.  This  is 
about  12%  higher  than  that  of  the  simple  turbine,  but  the 
important  difference  between  the  two  machines  lies  in  the 
fact  that,  while  the  simple  turbine  considered  has  a  peripheral 
speed  of  1200  feet  per  second,  and  a  ratio  of  initial  steam 
velocity  to  peripheral  velocity  of  2.9  to  1,  the  turbine  mth 
three  rotating  wheels  develops  power  with  about  equal  economy 
when  working  at  a  peripheral  velocity  of  400  feet  per  second,  or 
one  third  that  of  the  simple  turbine,  and  with  a  ratio  of 
peripheral  to  initial  steam  velocity  of  about  1  to  7.2.  It  is 
to  be  rememl^ered,  also,  that  the  simple  turbine  considered 
is  assumed  to  exhaust  into  a  condenser,  although  it  has  some- 
what low  nozzle  efficiency;  while  the  turbine  with  three  rotat- 
ing wheels  is  assumed  to  be  exhausting  at  about  atmospheric 
pressure.  This  was  done  in  the  present  example  in  order  that 
the  effect  of  adding  a  second  set  of  nozzles  and  three  more 
rotating  wheels  might  be  shown,  and  it  remains  to  investigate 
that  part  of  the  problem. 

Calculations  for  the  Second  Stage  of  the  Turbine. — From 
the  heat  diagram  it  was  found,  in  the  first  part  of  the  example, 
that  steam  in  expanding  adiabatically  from  160  to  14  pounds 
absolute  pressure  gave  up  178  B.T.U.  per  pound.     In  a  fric- 


THE  IMPULSE-TURBINE,  167 

tionless  and  otherwise  ideal  tnrl)ine  all  of  this  energy  would 
be  effective  in  producing  velocity  of  flow  in  the  nozzles.  The 
frictional  resistance  opposed  by  the  surfaces  of  nozzles  and 
buckets  causes  the  steam  to  give  up  less  heat  as  work  on  the 
buckets,  and  therefore  to  carry  awaj'  more  heat  into  the  ex- 
haust, than  it  would  in  a  frictionless  turbine.  The  useful 
work  done  upon  the  buckets  of  the  three  moving  wheels  con- 
sidered has  been  found  to  be  104,900  foot-pounds  per  pound 
of  steam.     This  is  equivalent  to  135  B.T.U. 

If  losses  caused  by  leakage  past  the  buckets,  and  by 
mechanical  friction,  windage,  etc.,  be  neglected,  the  steam  at 
exhaust  from  the  last  of  the  three  movable  buckets  will 
possess  an  amount  of  heat  greater  than  it  would  have 
possessed  after  purely  adiabatic  expansion,  equal  to  178  — 
135=43  B.T.U.  per  pound.  After  adiabatic  expansion,  if 
such  had  occurred,  from  160  to  14  pounds  absolute,  the  steam 
would  contain  1018  B.T.U.  per  pound,  and  its  cpahty  would 
be  0.868.  The  heat  of  vaporization  of  dry  saturated  steam 
at  14  pounds  absolute  is  967  B.T.U.  There  is  present  in 
each  pound  of  the  mixture  of  steam  and  water  1.00  —  0.868  = 
0.132  pound  of  water,  and  to  evaporate  this  would  require 
0.132  X  967  =  128  B.T.U.  The  amount  of  heat  available  for 
accompUshing  evaporation,  and  therefore  for  increasing  the 
quality  of  the  steam,  is  43  B.T.U.     This  is  sufficient  to  in- 

43 

crease  the  quaUty  by  r^X  0.132  =0.0443.      The  quality  of  the 

steam  entering  the  second-stage  nozzles  will  then  be  0.868  + 
0.044  =  0.912. 

Steam  of  14  pounds  absolute  pressure  and  0.912  quality 
contains  1060  B.T.U.  per  pound.  This  steam  is  to  expand 
in  the  second-stage  nozzles  to  a  final  pressure  corresponding 
to  a  vacuum  of  29  inches  of  mercury  or  a  temperature  of  540 
degrees  absolute.  Follo\\dng  the  vertical  line  on  the  heat 
diagram  from  the  state-point  for  the  steam  before  it  enters 
the  second-stage  nozzles  down  to  the  line  of  540  degrees  abso- 
lute temperature,  the  heat  contents  of  the  mixture  of  steam 


168  STEAM-TURBINES. 

and  water,  after  expansion,  is  875  B.T.U.  The  heat  avail- 
able for  producing  velocity  in  the  jet  from  the  second-stage 
nozzles  is  then  1060-875  =  185  B.T.U. 

The  heat  emplo^-ed  in  the  first  stage  was.  .   135  B.T.U. 

Total 320  B.T.U. 

The  total  heat  drop  during  expansion  of  dry  saturated 
steam  from  160  pounds  absolute  to  a  vacuum  of  29  inches 
is  320  B.T.U.,  in  case  the  quality  of  the  exliaust  is  as  indicated 
by  the  above  calculation,  that  is,  0.78.  The  quahty  after 
adiabatic  expansion  would  of  course  be  lower  than  this.  Let 
the  energy  loss  due  to  friction  in  the  second-stage  nozzles 
be  that  corresponding  to  a  value  of  y=0.26.  The  initial 
velocity  of  steam,  as  it  strikes  the  first  buckets,  will  then  be 

V  =  224\/l85  X  0.74  =  2620  feet  per  second. 

Let  the  values  of  y  for  the  second  stage  be  as  follows: 

During  passage  through  set  No.  1 y=0.05 

"     "    2 ?/  =  0.06 

"     "    3 y  =  0.08 

"  "  ''        "     "    4 ^  =  0.10 

''  "  "        "     "    5 y  =  0.12 

The  velocities  will   then  be  as  follows: 

^'=2820  feet  per  second,  as  already  found. 
vi"  =  2250\/r^  005  =  2190  feet  per  second. 

72"  =  lSOO\/l-0.06  =1745 

rg"  =  1400\/l-0.08  =  1345 

7/'  =  1070\/l-0.10  =  1015 

v^^'=  780v^l  - 12  =   730 

V^^  =  final  absolute  velocity  =  520 


r:      ( 


THE  IMPULSE-TURBIXE.  1G9 

As  the  losses  increase,  the  blade  angles  become  greater 
and  greater,  and  the  designer  may  decide  to  Hniit  the  size  of 
exit  angle.  Suppose,  for  example,  it  were  thought  advisable 
to  hmit  the  exit  angles  to  45°  or  less.  The  angle  of  T'^4"  would 
become  larger  than  4.5°  if  the  method  of  laying  out  the  dia- 
gram Aveie  not  changed.  A  line  X"L  may  be  rlrawn  making 
an  angle  of  45°  with  the  line  of  action  of  the  buckets,  and  z ■/' 
may  be  revolved  so  as  to  coincide  with  X"L.  Completing 
the  diagram  as  shown,  by  measuring  off  each  succeeding 
velocity  line,  as  v^'  upon  A"L,  the  corresponding  velocities 
may  be  found,  and  the  exit  angles  of  the  buckets  made  as 
desired.  A  similar  change  might  have  been  made  in  the  dia- 
gram for  the  first  stage,  and  would  have  resulted  in  smaller 
exit  angles  for  the  last  buckets.  This  would  have  shghtly 
increased  the  efficiency  of  the  first  stage,  but  that  it  would 
have  improved  the  turbine  as  a  whole  is  doubtful. 

The  work  done  by  the  steam  upon  the  moving  buckets 
of  the  second  stage  may  be  calculated  as  was  done  for  the  first 
stage. 

For  the  first  mo^'ing  buckets, 

^,,J2620)^-(180n,^-0.05x(2250)^^     52,200  ft.-pds. 

^^„J174o)^-a07a^-0.0Sx(1400)^^     27,000      " 

(1015F-(o2m^^0.12x(780F     ^     ^^.^     „ 
54.4  ' 

Total  work  of  second  stage 89,900  ft.-pds. 

Work  of  first  stage  of  turbine,  104,900,  say    105,000 


Total  work  of  turljine,  per  pound  of  steam,    194,900 

Taking  the  losses  due  to  friction  of  journals,  windage,  and 
leakage  as  22  per  cent   of  the  work  done  by  the  steam,  the 

c.x     .    X-      ■        1,980,000 
steam  consumption  oi  the  turbine  is  ■,„_  ^„„ — -r^z^  =  13  pounds 

19o,000x0./8         ^ 


170  STEAM-TURBIXES 

per  delivered  horse-power  hour,  approximately,  or  17.4  pounds 
per  K.W.  hour. 

These  calculations  are  based  upon  saturated  steam  at  the 
throttle-valve.  When  superheated  steam  is  used  the  losses 
are  much  lower  and  the  economy  correspondingly  higher. 
This  is  shown  in  the  tables  of  performance  of  the  various  tur- 
bines, the  steam  consumption  being  as  low  as  11.3  pounds 
per  electrical  horse-power  hour  when  operating  with  200  de- 
grees F.  superheat.     This  means  15.1  pounds  per  K.W.  hour. 

Up  to  this  point  nothing  has  been  said  as  to  the  amount 
of  power  the  turbine  is  to  develop.  It  has  been  shown  that 
the  steam  consumption  per  delivered  horse-power  at  the  tur- 
bine shaft  may  be  expected  to  be  13  pounds.  Tliis  economy 
refers  to  the  full-load  conditions,  and  the  steam  consump- 
tion will  increase  at  loads  below  and  above  full  loads.  If 
the  turbine  is  intended  for  operating  an  electric  generator 
having  an  efficiency  of  0.88,  the  steam  used  per  electrical 
horse-power  hour  will  be  14.8  pounds  at  full  load.  Tliis  will 
be  increased  by  from  15%  to  20%  at  50%  overload.  Taking 
the  increase  as  15%,  the  steam  consumption  at  50%  over- 
load will  be  about  17.4  pounds  per  electrical  horse-power 
hour. 

Let  the  turbine  be  required  to  operate  a  generator  deliv- 
ering 400  electrical  horse-power  at  full  load,  and  600  electrical 
horse-power  when  cahed  upon  for  maximum  overload.  The 
total  amount  of  steam  required  mil  be  c.s  follows: 

Full  load,  TF  =  14.8X400  ^3600  =  1.65  pounds   per  second. 

At  50%  overload,  TF'  =  17.4x600  ^3600  =  2.9  pounds  per 
second. 

To  find  the  diameter  of  the  turbine  wheels,  and  the  area  for 
passage  of  steam  through  the  second-stage  nozzles. — The  peri- 
pheral velocity  of  buckets  having  been  decided  upon  during 
the  design  of  the  buckets,  the  rate  of  revolution  of  the  turbine 
fixes  the  diameter  of  the  wheels.  Let  the  R.P.M.  be  2000. 
Then  for  a  peripheral  velocity  of  400  ft.  per  second  the  mean 
diameter  of  bucket  circle  will  be 


THE  IMPULSE-TURBINE.  171 

Q  ]^^^9QQQ  =  3.82  feet  or  46  inches. 

It  has  been  assumed  in  the  present  problem  that  the  steam 
pressure  at  entrance  to  the  second-stage  nozzles  will  be  14 
pounds  absolute.  The  second-stage  nozzles  will  be  non-expand- 
ing, while  those  of  the  firet  stage  will  be  expanding  nozzles. 
The  pressure  in  the  throat  of  the  second -stage  nozzles  will  be 
about  .577 X 14  =  8.10  pounds  absolute.  The  total  loss  of  energy 
in  these  straight  nozzles  has  been  assumed  to  be  that  corres- 
ponding to  2/ =  0.26  (see  page  168).  Assuming  that  the  steam 
expands  to  the  shell  pressure  before  entering  the  first  row  of 
buckets  in  the  second  stage,  the  initial  velocity  has  been  shown 
to  be  2620  feet  per  second  (see  page  168).  But  this  is  not 
the  velocity  in  the  entrance  or  orifice  of  the  nozzles.  Let  the 
friction  loss  in  the  orifice  be  represented  by  y  =  0.08.  The  heat 
contents  at  entrance  to  the  nozzles  is  1060  B.TA^.  per  pound. 
The  steam  is  to  fall  in  pressure  at  once  upon  entering  the 
nozzles,  to  8.1  pounds,  and  to  be  dried  to  a  certain  extent  dur- 
ing this  drop  in  pressure.  The  initial  quality  is  0.912  (page 
167),  and  if  the  expansion  to  8.1  pounds  shouid  be  adiabatic 
the  heat  diagram  shows  that  the  quality  in  the  orifice  would 
be  a:' =  0.885  and  the  heat  contents  1023  B.T.U.  per  pound. 
Since  the  heat  of  vaporization  at  8.1  pounds  absolute  is  986, 
the  increase  in  quantity  due  to  the  heat  of  friction  will  be 
x"  =  .08(  1060  - 1023)  4-  986.  =  0.003  (see  page  83) .  The  quality 
in  the  orifice  will  then  be 


x'+x"  =0.885 +0.003  =  0. 
The  corresponding  heat  contents  is  1028  B.T.U.  per  pound. 
The  velocity  in  the  orifice  is  224\/(1060- 10J8)  =  1255  feet  per 
second.  Since  the  specific  volume  of  dry  steam  at  8.1  pounds 
absolute  is  47  cubic  feet  per  pound,  that  at  0.888  quality  will 
be  47.0x0.888  =  41.7  cubic  feet.  The  necessary  cross-sectional 
area  of  the  orifices,  collectively,  will  then  be 

.     2.9X41.7X144     ^^^ 
A= r^V;. =  13.9  square  mches. 


172  STEAM-TURBINES. 

The  nozzles  through  which  the  steam  expands  into  each 
shell  of  the  turbine  are  ordinarily  of  four-sided  cross-section, 
slightly  roimding  at  the  throat  in  some  cases;  but  each  nozzle 
presents  a  four-sided  outlet  (ABCD,  Fig.  64),  next  to  the  first 
row  of  buckets.     The  radial  walls  are  often  fomied  of  steel 


Fig.  63. 

plate  about  A  inch  thick,  cast  into  the  nozzle  frame  as  shown 
in  Fig.  63. 

The  general  arrangement  of  turbine  casing  and  nozzles  is 
shown  diagrammatically  in  Fig.  64,  the  pitch  of  nozzles  being 
greatly  exaggerated  in  this  diagram.  The  steam  is  led  into  the 
first  stage  of  the  turbine  through  expanding  nozzles,  and  into 
the  succeeding  stage  or  stages  through  straight  nozzles,  of 
uniform  cross-sectional  area.  These  nozzles  are  short,  and  the 
exit  ends  are  cut  off  parallel  to  the  plane  of  wheel  rotation. 

The  first-stage  nozzles  may  occupy  only  a  small  part  of  the 
annular  space  available  for  them;  but  in  the  final  stage,  owing 
to  the  great  volume  of  steam  to  be  passed,  it  may  be  necessary 
to  utilize  the  entire  available  space.  If  the  turbine  should  be 
small  in  diameter,  comparatively,  the  nozzles  might  require  to 
be  of  such  height  radially  that  the  buckets,  especially  the  last 
row  of  the  stage,  would  be  higher  than  good  practice  permits. 
The  whole  circumference  is  not  ordinarily  available  for  nozzles, 
because  of  structural  conditions;  for  example,  the  diaphragms 
may  be  made  in  halves,  and  the  flanges  for  joining  the  two 
parts  take  up  some  space.  In  any  case,  there  is  a  certain  angle 
at  the  center  of  the  shaft,  which  can  conveniently  be  subtended 
by  the  nozzles.  The  latter  may  be  disposed  in  two  groups, 
each  subtending  half  the  total  angle  available,  one  group  being 


THE  IMPULSE-TURBINE. 


173 


in  each  haK  of  the  diai)hragm.  It  becomes  necessary  to  deter- 
mine the  height  H  which  the  nozzles  must  have,  to  afford  the 
requisite  cross-sectional  area  of  stcain  passage. 

Referring  to  Fig.  64,  the  angle  A  which  the  design  permits 
the  nozzles  to  subtend,   and  the  other  particulars  to  which 


'M;=<>-rsin  a 


FiG^  64. — Diagrammatic  representation  of  nozzles  in  a  Curtis  tmbine.     The 
pitch  of  nozzle  walls  is  purposely  exaggerated. 

symbols  have  been  given,  are  related  to  each  other  in  the  fol- 
lowing manner.  The  fraction  of  the  pitch  of  nozzles,  p,  which 
represents  clear  opening  in  an  axial  direction  (axial  with 
respect  to  the  turbine  axis)  is 

V 


174  STEAM-TURBINES. 

But  iv  = and  therefore  k  =  l  — 


sin  a  p  sin  a 

Supposing,  for  example,  a  turbine  having  a  pitch  diameter  of 
46  inches,  as  in  the  present  example,  should  have  nozzle  walls 
made  of  xVinch  plate,  and  that  the  angle  a  =  20°  for  the  nozzles 
of  the  last  stage.    Let  the  pitch,  p,  =1.46  inches. 

This  means  that  the  nozzle  walls  occupy  12|%  of  the  space 
devoted  to  nozzle  openings  in  front  of  the  buckets. 

The  nozzles,  as  a  whole,  subtend  an  angle  of  J  degrees  at 
the  center  of  the  diaphragm,  and  the  whole  length  of  arc  of  pitch- 

TtDJ 

circle  included  by  the  angle  J  is-o7v7  inches.     Then  the  mean 

net  length  of  the  space  occupied  by  nozzle  outlets,  after  taking 
out  the  area  occupied  by  the  ends  of  the  nozzle  walls,  is  equal  to 

knDJ 


360 


The  area  perpendicular  to  the  direction  of  steam  flow  through 
the  nozzles  is,  then, 

knDAH  sin  CY      „    ^ -r^-r.,  .    . 

A  = -^ ,=0.0087HDkJ  sin  a. 

Applying  this  to  the  case  in  hand,  the  required  area  A  is 
13.9  square  inches;  Z)  =  46  inches;  a  =20°;  sin  a  =0.342.  Let 
the  angle  J  =  120°.  The  necessary  height  of  nozzles  will  then 
be 

^  =  0.0087x46X0.875X120X0.342  =  ^-^^  ^^'^''• 

The  height  of  the  buckets  nearest  the  outlet  end  of  the 
nozzles  is  made  about  2^%  greater  than  the  nozzle  height. 
This  would  make  the  first  row  of  buckets  in  the  present  case 


THE  IMPULSE-TUREINE.  175 

0.995,  or  approximately  1  inch  high  at  the  steam-inlet  side.  The 
ratio  between  the  maximmn  height  of  the  last  row  of  buckets 
in  a  given  stage  and  the  minimum  height  of  the  first  row,  is 
called  the  "height-ratio."  If  this  should  be  made  equal  to 
2,  in  the  present  case,  the  maximum  height  of  the  last  bucket 
would  be  2  inches. 

The  meaning  of  the  term  "  height-ratio"  will  be  understood 
by  reference  to  the  figures  on  page  163.  The  relative  areas 
for  passage  of  steam  through  the  successive  rows  of  buckets 
are  of  more  value  than  are  the  height- ratios;  but  the  latter, 
with  given  bucket-shapes  and  spacing,  serve  as  something  of 
an  indication  of  the  value  of  area  ratios. 

Efficiency  of  steam  turbines.  Design  of  impulse-turhines  on 
the  basis  of  experimentally  determined  stage  efficiency.  Heat 
analysis  of  steam  turbines. — Steam-turbine  efficiency  is  ordi- 
narily expressed  as  the  ratio  of  the  work  actually  delivered 
from  the  turbine  shaft  per  unit  of  time,  to  that  ^^  hich  ^^  ould 
have  been  delivered  if  the  steam  had  expanded  adialmtically, 
and  the  total  energy  available  from  such  expansion  had  been 
transformed  into  mechanical  work.  As  an  example,  suppose 
the  initial  steam  pressure  to  be  165  pomids  absolute  per  square 
inch,  and  that  the  steam  were  superheated  100  degrees  F. 
From  the  chart  at  the  back  of  the  book  the  steam  AA'ould  con- 
tain, in  its  initial  condition,  1252  B.T.U.  per  pound.  If  the 
steam  should  expand  adiabatically  to  a  pressure  of  1  pound 
absolute  (562  degrees),  its  fijial  heat  contents,  found  by  passing 
down  an  adiabatic  line  on  the  chart  to  562  degrees,  would  be 
910  B.T.U.  A  perfect  engme  would  deliver  mechanical  energy 
equivalent  to  the  difference  in  heat  contents  between  the  initial 
and  final  states  of  the  steam,  and  would  completely  utilize, 
therefore,  1252-910  =  342  B.T.U.  per  pound  of  steam  used. 
This  is  called  the  available  heat,  H,  ))er  pound  of  steam,  and  is 
equivalent  to  778  H,  foot-pounds,  or,  in  this  case, 
778X342=266,076  foot-poutids. 

Since  the  expression  "one  horse-power"  means  an  expendi- 
ture of  33,000  foot-jiounds  per  minute,  or  1,980,000  foot-pounds 


176 


S  TEA  M-  T  URBINES. 


per  hour,  the  number  of  pounds  of  steam  which  a  perfect  engine 
would  require  per  horse- power  hour  under  the  above  condi- 
tions, is 

1,980,000     ^ ,  .      ,  - 

2QQ07Q  approximately. 

If  an  actual  engine,  operating  under  the  same  conditions, 
uses  13  pounds  of  steam  per  delivered  horse-power  hour,  its 
efficiency  is  7.4-^13=0.57. 

The  efficiency  of  any  steam  engine  may  be  calculated  in  a 
similar  manner,  from  results  of  tests;   thus 


Efficiency  = 


1,980,000 


water   rate  X  available  energy  in  foot  pounds   per 
pound  of  steam  per  hour. 


The  table  given  below  shows  the  use  which  may  be  made 
of  such  calculations  in  determining  the  effect  upon  efficiency 
produced  by  varying  conditions  of  operation. 

Calculathig  from  the  ^^  ater  rates  given  below  the  variation 
of  efficiency  with  load  and  with  superheat  is  shown  in  the 
following  table.     (Particulars  of  turbine  given  below.) 


100°  Superheat. 

Saturated  Steam. 

Test 
No. 

B.H.P. 

W.R. 

Effic.=7.8-^W.R. 

Test 

1   No. 

B.H.P. 

W.R. 

Effic.  =  8.35  H- W.R. 

1 
2 

3 
4 
5 
6 

269. 
402. 
649. 
766. 
956. 
1195. 

16.2 
14.6 
13.3 
13.1 
13.5 
14.1 

.481 
.534 
.586 
.595 
.577 
.553 

1 
2 
3 

4 

5 

245. 
406 . 
6.50. 
716. 
1144. 

19.4 
16.2 
14.6 
14.7 
15.7 

.430 
.516 
.572 
.568 
.532 

Westinghouse-Parsons  400  K.W.  Steam  Turbine,  3600 
R.P.^I.,  with  automatic  by-pass  valve.  Work  absorbed  by 
water-brake.  Tests  to  determine  economy  to  be  gained  by  use 
of  100°  F.  superheat.  Steam-pressure  in  main  steam-pipe  150 
pounds  gage  or  165  pounds  absolute  in  both  cases  below. 
Vacuum  27  inches  in  both  cases.     Bucket  speed  varying  from 


THE  IMPULSE  TURBINE. 


177 


157  feet  per  second  at  H.P.  end  to  345  feet  per  second  at  L.P. 
end.    Available  energy  at  100°  superheat,  assuming  adiabatic 


30 

11 

\ 

\ 

\ 

28 

i 

1         \ 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

\ 

Eff 

1,980,000 

E.  X  W.R 

—  26 

y 

\ 

\ 

\ 

\ 

^\ 

\ 

\ 

\ 

\ 

\ 

\ 

K 

24 

I 

\\ 

\ 

\ 

\\ 

\ 

\ 

A 

\, 

\ 

\  \ 

9! 

\ 

\ 

\ 

1 
-=-20 

33 

\ 

\ 

\ 

A 

\ 

\ 

\\ 

\ 

c 

\ 

\ 

> 

\\ 

\ 

\ 

\ 

\\\ 

\\ 

\ 

\ 

^\ 

^^ 

\ 

\          \ 

\\ 

\ 

\ 

\ 

! 

m 

\ 

V 

\ 

\ 

\ 

^14 

A 

A 

\ 
\ 

\ 

WV3 

A  A 

\^ 

\ 

\ 

\ 

^ 

A 

\ 

\ 

\ 

\ 

\ 

\^ 

^\ 

\ 

\ 

\ 

\ 

\ 

.20 

.40 

.00 
Efficiency 

.80 

1.00 

Fig.  65. — Curves  of  Efficiency  and  Water-rate  for  given  Available  Energy. 

expansion  to  27  inches  vacuum  =326  B.T.U.  or  254,000  foot- 
pounds per  pound  of  steam. 


178 


STEAM-TURBINES. 


Efficiency  =^  ^ -^  ^^^^  ^^^  =  7.8  -^  W.R.  where   W.R.  = 
pounds  steam  per  B.H.P.  hour.    With  saturated  steam,  and 


2400. 

R.P.M 

Ht^  100. 

200.    1     300. 

4 

10. 

5( 

lO. 

6 

)0. 

roo. 

1 

8 

0. 

9( 

'0. 

100 

), 

■TlQO 

|\ 

V 

'to   •- 

"a 

\ 

X 

-•'000  *> 

\ 

N 

X 

s 

180( 

)  ^ 

S 

K 

N 

K 

-160C 

1   m 

\ 

\ 

s 

\ 

N 

k 

-1401 

o 

a. 

\ 

N 

X 

N 

\ 

•120( 

\ 

\^ 

\ 

-20- 

\ 

\ 

i 

\ 

.bO 

\ 

-;68 

-18.- 

\ 

\ 

^ 

^ 

^ 

T56 

\ 

.^s 

y 

-17.- 
-16.- 

o 
S- 

16-00.  Pounds  Steam  Flowing  per  Hour.    ^ 

V. 

A 

y 

> 

-50 
-748 
-t46 

28,Inches  Vacuum.                                                  \ 

/ 

/ 

o 
C 

® 

259.000.FootPoundsAvailable  Energy,  per 

Pound  Steam. 

Condition  of  Steam  at  Entiance.Diy  Satur 

/ 

K 

o 

ijed. 

\ 

\ 

w 

-15r 

S- 

/ 

N 

s  ^l 

-44- 

A 

/ 

i^^. 

14.- 

/ 

/ 

^ 

^^, 

(0 

•3 

/ 

^\ 

..^ 

-13r 

3 
O 

A 

/ 

-36 

/ 

1-2. 

1( 

0. 

2C 

0. 

3( 

0./ 

4( 

0. 

5{ 

0. 

6( 

0. 

7C 

0. 

8( 

0, 

oc 

0. 

100 

). 

R.P.M. 


Fig.  66. — Curves  of  Efficiency  and  Water-rate  as  Computed  from 
Experimentally  Detemiined  Torque  Line. 

same   vacuum,    available    energy  =  237,000  foot-pounds,    and 
efficiency  =  vv.li^SoO  "  ^'^^  "  ^^■^- 


THE  IMPULSE  TURBINE.  179 

The  efficiency  corresponding  to  a  given  amount  of  available 
energy,  and  given  water-rate,  may  be  found  approximately  from 
the  curves  in  Fig.  65,  without  calculation. 

If  a  Ijrake  has  been  used  to  absorlj  and  measure  the  work 
done  by  a  turbine,  a  "torque-line"  may  be  plotted  from  the 
results  of  the  test,  as  shown  in  Fig.  66.  With  a  given  con- 
stant rate  of  steam  flow  the  pull  on  the  brake-arm  varies 
inversely  as  the  speed  of  revolution  of  the  turbine.  If  the 
shaft  be  brought  to  rest  by  the  brake  and  the  steam  caused 
to  pass  through  the  turbine  as  before,  the  pull  on  the  brake  is 
greater  than  when  the  shaft  is  in  motion.  This  is  called  the 
"standing-torque."  If  the  shaft  is  permitted  to  rotate,  the 
torque  decreases  uniformily  with  increase  of  speed  of  rotation. 
The  torque-line  is  straight  in  all  cases,  as  shown  in  Fig.  66. 
From  the  torque-line  and  other  results  of  tests,  cuitcs  of  water- 
rate  and  efficiency  may  be  plotted,  based  upon  such  calculations 
as  are  outlined  below. 

Let         P.  =pull  on  brake-arm,  pounds. 
B.H.P.  =brake  horse  power. 

T7  =  pounds  of  steam  per  hour,  total. 
W.^.= water-rate,  or  pounds  of  steam  per  B.H.P.-hour. 
E.  =  available    energy,    foot-pounds    per  pound    of 
steam  used. 
E^.  =effiiciency  of  turbine,  or  of  the  part  tested. 
r,  =  length  of  brake-arm,  feet. 
i^.P.M.  =  revolutions  per  minute. 

TV,.n                   R77P     2;rrPX(R.P.M.) 
Then,  B.H.P..= 33000        , 

33,000  W 


W.R,= 


2;rrPx(R.P.M.)' 


j>  4.  -uTT^     ^        1,980,000 

But  W.R.^ho  =  -^^^^. 


180 


STEAM-TURBIXES. 


Therefore 


1,980,000  33,000  W 


Eff.xE      2;:rPX(R.P.M.)' 


1 ,980,000  X  27trP  X  (R.P.M.)     377rPx  (R.P.M.) 
and     Eff.-  33,000  TFx^  ^  TfX^ 

To  illustrate  the  use  of  this  expression  for  efficiency,  sup- 
posing a  torque-line  such  as  is  shown  in  Fig.  66,  has  been 
obtained,  and  curves  of  efficiency  and  water-rate  are  to  be 
plotted  from  it.  Let  r  =  5.25  feet;  TF  =  16,700  pounds  per  hour; 
.E= 259,000  foot-pounds  available  per  pound  of  steam.  The 
revolutions  per  minute  and  the  corresponding  values  of  P  are 
taken  from  the  torque-line. 


R.P.M. 


400 

600 

800 

1000 


1925 
1690 
1460 
1230 


Eff.= 


377.rPX  (R.P.M.) 
WXE 


.353 
.465 
.535 
.563 


W.R.= 


1.980.000 
EfF.X.B.  ■ 


21.7 
16.4 
14.3 
13.6 


The  efficiency  of  complete  turbines,  and  also  of  component 
stages  if  tested  by  themselves,  may  be  ascertained  in  the  man- 
ner indicated.  From  a  knowledge  of  the  efficiency  of  the  com- 
ponent parts  of  a  turbine  under  working  conditions,  calculations 
may  be  made  as  to  the  probable  efficiency  of  proposed  combi- 
nations of  those  parts  into  complete  turbines.  The  Rateau 
and  Curtis  types,  consisting  of  a  number  of  separate  wheels,  each 
in  a  separate  compartment,  are  especially  well  adapted  to  such 
analysis.  In  an  experimental  turbine,  specially  arranged  for 
the  purpose,  each  stage,  consisting  of  a  set  of  nozzles  and  one 
or  more  sets  of  buckets,  may  be  tested  by  itself.  Or  certain 
stages,  if  not  each  one  by  itseK,  may  be  taken  to  represent 
average  conditions,  and  the  efficiency  and  capacity  of  the  vari- 
ous stages  and  combinations  of  stages  may  be  ascertained  by 
a  properly  arranged  series  of  tests. 

In  the  calculations  for  efficiency  given  above,  the  loss  by 
friction  of  the  shaft  in  the  bearings,  etc.,  is  included.  This 
should  ob\nously  be  allowed  for  only  once  in  a  complete  turbine. 


THE  IMPULSE  TURBINE.  181 

and  not  in  connection  with  each  stage  tested.  The  efficiency 
of  each  stage  may  be  calculated  on  the  basis  of  "  bucket  horse- 
power,"  or  the  power  represented  by  the  pull  on  the  buckets, 
independently  of  the  mechanical  friction  and  the  windage  losses, 
these  being  astertained  by  separate  experiments. 

During  the  development  of  the  turbine,  experience  accumu- 
lates indicating  the  number  of  compartments  or  stages  to  be 
given  to  impulse  turbines,  and  the  number  of  "  steps-up  "  in 
diameter  of  turbines  of  the  Parsons  type.  In  general,  as  higher 
initial  pressures  and  degrees  of  superheat  are  used  the  number 
of  stages  is  increased.  Such  particulars,  and  those  concerning 
the  number  of  rows  of  movable  and  stationary  buckets  to  be 
used  in  each  stage  of  impulse  turbines  in  order  that  certain 
efficiences  may  be  obtained;  the  magnitude  and  variation  of 
bucket  angles  best  suited  to  the  energy  distribution  aimed  at 
in  the  various  stages;  the  proportions  of  nozzles,  and  the  relative 
heights  of  nozzles  and  buckets, — such  questions  are  determined 
by  experiment,  calculation,  and  scientific  research  of  various 
kinds  concerning  the  action  of  the  steam  as  it  passes  through 
the  turbine.  With  all  types  of  steam-turbine  at  present  under 
development  such  work  is  being  done,  and  refinements  in 
methods  of  analysis,  calculation,  and  construction  are  resulting 
in  improvement  in  economy  and  in  operation. 

As  an  example  of  the  way  in  which  steam-turbines  may  be 
proportioned  upon  the  basis  of  such  investigations  as  have  been 
discussed  in  the  preceding  paragraphs,  let  it  be  decided  to 
design  a  turbine  of  the  several  stage,  velocity-compounded  t^'pe. 
The  efficiency  of  the  different  stages  at  various  buckets-speeds 
may  be  supposed  to  have  been  determined  and  plotted  in  the 
form  of  curves  showing  the  variation  of  efficiency  ^ith  bucket- 
speed  and  available  energJ^ 

The  question  of  rate  of  revolution  and  corresponding  bucket- 
speed  determines  the  diameter  of  the  turbine  wheels.  The 
revolutions  are  decided  upon  according  to  the  speed  at  which 
it  is  desired  to  rotate  the  shaft  of.  for  example,  a  generator,  or 
propeller  wheel  to  which  the  turbine  is  to  be  connected.  The 
efficiency  is  directly  dependent  upon  bucket-speed  and  available 


182  STEAM-TURBINES. 

energy.  The  efficiencies  it  is  necessary  to  use  are  those  ob- 
tained experimentally  with  buckets  and  nozzles  similar  to  those 
to  be  used  in  the  proposed  turbine.  It  should^  therefore,  be 
possible  to  predict  closely  what  each  stage  will  do  in  the  com- 
pleted machine.  The  first  stage  of  a  velocity-compounded 
turbine  may  be  given  such  bucket  angles  and  such  a  number 
of  rows  of  buckets  that  it  will  absorb  a  greater  percentage  of 
the  available  energy  than  is  absorbed  by  any  one  of  the  suc- 
ceeding stages.  The  efficiency  of  the  first  stage  may  be  some- 
what lower  than  that  of  the  others,  but  as  it  is  affected  by  a 
greater  heat  drop  than  is  allowed  in  the  other  stages,  the  work 
done  by  the  first  is  in  general  greater  than  that  done  by  any 
other  stage. 

In  order  to  proportion  the  steam-nozzles  leading  from  each 
compartment,  or  shell,  to  the  next,  so  as  to  obtain  the  energy 
distribution  aimed  at  in  the  turbine,  calculations  are  made  as 
shown  in  tabular  forms  A  and  B  on  pages  183-184.  The  results 
of  these  calculations  relate  to  the  condition  of  the  steam  as  to 
pressure,  quality,  temperature,  etc.,  at  the  entrance  to  the 
nozzles  of  each  stage.  From  this  information  the  cross-sectional 
areas  of  the  nozzles  are  determined  so  that  the  requisite  amount 
of  steam  may  be  discharged  into  the  buckets,  per  unit  of  time, 
to  give  the  desired  horse -power. 

The  general  scheme  of  calculation  is  similar  to  that  used  in 
the  example  worked  out  on  more  completely  theoretical  lines, 
on  pages  158  to  173,  but  in  the  present  case  there  is  no  attempt 
to  definitely  locate  and  allow  individually  for  the  frictional  and 
other  losses  in  each  stage.  The  experimentally  determined 
stage  efficiency  takes  account  of  all  losses  excepting  windage 
and  shaft  friction,  which  are  allowed  for  separately,  and  avoids 
the  necessity  of  detailed  analysis. 

The  principle  follow^ed  in  calculating  for  the  steam  condi- 
tion in  the  various  stages  is  as  follows:  Steam  possessing  a 
known  amount  of  available  energy  per  pound  is  supposed  to 
drop  in  pressure  and  temperature  during  its  passage  through 
each  stage  until  it  gives  up  a  certain  predetermined  proportion 
of  its  available  energy.     This  drop  is  supposed  to  take  place 


THE  IMPULSE  TURBINE. 


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STEAM-TURBINES. 


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THE  IMPULSE  TURBINE.  185 

adiabatically.  But  all  of  the  energy  given  up  in  any  one  stage 
does  not  appear  as  work  delivered  by  that  stage.  That  which 
does  not  appear  as  work  is  assumed  to  be  given  back  to  the 
steam  to  dry  it  at  constant  pressure  in  case  moisture  has  ap- 
peared, or  to  superheat  it,  also  at  constant  pressure,  in  case 
the  steam  has  not  yet  become  wet.  The  amount  of  the  reheat 
(disregarding  radiation,  conduction,  and  leakage  losses),  is  rep- 
resented by  {\  —  e)hs,  where  e  is  the  stage  efficiency  and  h^  is  the 
heat  drop  in  the  stage  under  consideration. 

Let  the  turbine  be  required  to  develop  2000  horse-power  at 
1000  revolutions  per  minute,  and  let  the  mean  bucket-speed  be 
420  feet  per  second.  The  mean  diameter  of  bucket  circle  will 
then  be 

420X60 
^     1000X3.14    *^''^'^' 

Let  the  initial  pressure  and  degree  of  superheat  be,  respec- 
tively, 165  pounds  absolute  and  100°  F.  Let  the  pressure  in  the 
exhaust  pipe  be  1  pound  absolute  or  correspond  to  28  inches 
vacuum.  From  the  heat  diagram,  the  heat  contents  at  entrance 
to  the  first  nozzle-bowls  is  77^^  =  1252  B.T.U.;  and  the  final 
heat  contents  after  adiabatic  expansion  to  1  pound  absolute  is 
fi^2  =  910  B.T.U.  The  available  energy,  assuming  adiabatic 
expansion,  is  therefore 

^  =  i75, -772  =  1252 -910  =  342  B.T.U. 

Let  the  turbine  have  six  stages,  and  let  the  energy  distribu- 
tion aimed  at  be  as  follows: 

First  stage,  0.30  E=hs^  =  102  B.T.U.,  approximately. 

Remaining  stages,  0.14  E  =  hs2,  K^,  etc.  =  48  B.T.U.,  " 
Let  the  stage  efficiencies  be  taken  from  experimentally  deter- 
mined curves,  as   0.48  for  the  first  stage,  and  0.55  for  each 
remaining  stage. 

It  is  now  possible  to  use  a  heat-diagram  to  ascertain  the 
probable  steam  condition  as  to  pressure,  temperature,  quafity, 
heat-contents,  etc.,  at  the  various  nozzle-bowls,  and  to  use  this 
information  in  determining  the  areas  of   cross  section  of  the 


186  STEAM-TURBINES. 

various  sets  of  nozzles.  The  method  of  making  calculations  is 
shown  below,  and  the  heavy  lines  in  the  heat-diagram  on  the 
back  cover  of  the  book  show  the  calculated  expansion  cui-ve. 

All  results  in  these  calculations  are  in  B.T.U.  per  pound  of 
steam. 

Initial  heat  contents,  per  pound  of  steam 1252  B.T.U. 

Adiabatic  drop  in  first  stage  nozzles 102 

1150 
Reheat  in  first  stage  (1  -0.48)  X  102 53 

Heat  contents  at  entrance  to  second  stage  nozzles 1203 

Adiabatic  drop  in  second  stage  nozzles 48 

1155 
Reheat  in  second  stage  (1  -0  55)  X48 22 

Heat  contents  at  entrance  to  third  stage  nozzles 1177 

Adiabatic  drop  in  third  stage  nozzles 48 

1129 
Reheat  in  third  stage  (same  as  in  second  stage) 22 

Heat  contents  at  entrance  to  fourth  stage  nozzles 1151 

Adiabatic  drop  in  fourth  stage 48 

1103 
Reheat  in  fourth  stage 22 

Heat  contents  at  entrance  to  fifth  stage  nozzles 1125 

Adiabatic  drop  in  fifth  stage  nozzles 48 

1077 
Reheat  in  fifth  stage 22 

Heat  contents  at  entrance  to  sixth  stage  nozzles 1099 

Adiabatic  drop  in  sixth  stage  nozzles 48 

1051 
Reheat  tn  sixth  stage 22 

Heat  contents  of  exhaust 1073 

Heat  actually  given  np,  per  pound  of  steam,  1252—1073=  179  B.T.U. 
Heat  that  would  have  been  given  up  during  adiabatic  ex- 
pansion     342       " 

179 
Efficiency,  —  =  .524. 

The  water-rate  based  on  this  efficiency  would  be  - ''  ^'-j~o  =  14.2  pounds. 

The  efficiencies  selected  above  for  the  stages  have  been 
taken  at  random,  and  do  not  necessarily  represent  the  per- 
formance of  any  particular  turbine. 


THE  IMPULSE  TURBINE.  187 

It  is  to  be  notcil  that  the  final  temperature  and  pressure  of 
the  steam,  as  shown  by  the  expansion  curve  on  the  heat-dia- 
gram, are  slightly  above  the  vacuum  conditions  assumed.  A 
difference  of  this  kind  will  always  be  found  in  the  calculations 
when  the  steam  in  its  final  condition  is  moist,  and  the  difference 
is  dependent  upon  the  eflficiencies  assumed  and  the  heat  distri- 
bution employed.  The  efficiencies  used  in  the  present  example 
may  be  assumed  to  take  into  account  dissipation  of  energy  by 
shaft  friction,  windage,  leakage,  etc.,  and  the  calculated  water- 
rate  therefore  to  be  in  pounds  of  steam  per  B.H.P.  hour. 

In  order  to  find  the  height  of  nozzles  and  buckets  in  the 
last  stage,  or  in  fact  of  any  one  of  the  stages,  the  steps  to  be 
taken  are  similar  to  those  described  on  pages  170-173.  Thus, 
the  area  required  through  the  nozzles  of  the  last  stage  is  227 
square  inches,  to  provide  for  2000  horse-power.  In  case  it  is 
desired  to  provide  for  an  overload  of  50%,  nozzles  may  be 
added  which  can  be  opened  by  valves  suitably  arranged.  Sup- 
posing it  is  desired  to  provide  for  a  possible  overload  of  50% 
and  that  when  so  overloaded  the  turbine  will  require  10% 
more  steam  per  horse-power  hour  than  is  required  at  normal 
load,  the  area  of  nozzles  to  be  provided  must  be  increased  to 
375  square  inches. 

Let  the  thickness,  t,  of  nozzle  walls  be  ^  inch  and  let  the 
angle  of  nozzles  with  the  plane  of  rotation  be  25  degrees, 
(sin  25°  =  0.423.)  Let  the  pitch  of  nozzles  be  1.5  inches,  and 
let  the  nozzles  subtend  an  angle  at  the  center  of  the  shaft  of 
i  =  180°.  Assuming  that  it  is  not  practicable  to  make  one  set 
of  nozzles  occupy  half  the  pitch  circle,  on  account  of  the  bolt- 
ing together  of  the  diaphragm,  let  the  nozzles  be  made  in  two 
sets,  each  subtending  90°  and  on  opposite  sides  of  the  turbine. 
The  height  of  nozzles  in  the  last  stage  will  then  be 

"  =0.0087  X  96X  O^g'fsx  180  xO.423  =  "'^  '"^'^^  "'^■''y- 

It  is  to  be  noted,  that  while  the  nozzles  leading  into  all 
the  compartments  excepting  the  first  are  non-expanding,  the 


188  STEAM-TURBINES. 

velocity  of  steam  from  these  nozzles  is  supposed  to  be  that 
corresponding  to  the  heat-drop  from  one  stage  to  the  next  and 
the  nozzle  efficiency,  and  not  merely  the  orifice  velocity  from 
which  the  area  is  determined.  That  is,  the  steam  is  supposed 
to  be  accelerated  after  it  leaves  the  orifice,  or  entrance  to  the 
straight  nozzles.  In  this  connection  reference  should  be  made 
to  the  experimental  work  discussed  in  Chapter  VI,  where  it  is 
shown  that  for  initial  pressures  less  than  about  80  pounds  ab- 
solute the  straight  nozzle  is  fully  as  efficient,  if  net  more  so, 
than  the  expanding  nozzle. 


Superheat,  E)«g.  F, 


CHAPTER    Mil 
THE  IMPULSE-AND-REACTIOX  TURBINE. 

As  an  introduction  to  the  study  of  the  Parsons  turbine 
reference  should  l)c  made  to  the  descriptive  matter  on  pages 
251  to  270,  including  figures  86  to  100.  Before  attempting  to 
analyze  the  turbine  on  the  basis  of  velocity  diagrams,  and 
before  taking  up  the  question  of  frictional  resistances,  reheat, 
and  the  location  of  the  various  losses  of  energy,  a  simple 
example  will  be  worked  out,  assuming  adiabatic  expansion 
throughout  the  turbine. 

Let  it  be  decided  to  design  a  turbine  of  1000  B.H.P.,  taking 
steam  at  175  pounds  absolute  pressure  per  square  inch  and 
160°  F.  superheat  at  the  throttle,  and  expanding  it  to  a  vacuum 
represented  by  28  inches  mercury. 

The  initial  heat  contents  are  found  from  the  heat-diagram 
to  be  1288  B.T.U.  per  poimd,  =  //i.  The  final  heat  contents, 
after  adiabatic  expansion  to  vacuum  conditions,  are  similarly 
found  to  be  925  B.T.U.  per  pound,  =  i/2. 

Available  energy  =  i/i  —  i72  =  363  B.T.U.  per  pound. 

Let  it  be  decided  to  make  the  ratio  of  peripheral  velocity, 

?<,  to  steam  velocit}-,  V,  equal  to  x?  =  0.60.* 


*  It  should  be  noted  here  that  if,  with  a  given  constant  value  of  u  the  ra'  ".o 
—  be  increased,  the  velocity  V  is  necessarily  decreased.  V  varies  directly 
as  the  square  root  of  the  heat  given  up  per  stage  by  the  steam,  hence  there 
is  less  and  less  energy  given  up  per  stage  as  the  ratio -r?  is  increased.  There- 
fore the  number  of  stages  necessary  in  order  to  absorb  a  given  supply  of 
available  eneigy  increases  as  the  ratio  -p  increases,  for  a  given  constaiit 
value  of  u. 

189 


190 


STEAM-TURBINES. 


Let  it  be  similarly  decided  to  allow  a  mean  peripheral  velocity 
of  blades  in  the  first  cylinder  (see  page  217  for  definition  of  "cyl- 
inder") of  150  feet  per  second,  and  let  the  values  for  the  second 
and  third  cylinders  be  respectively  240  and  350  feet  per  second. 
The  steam  velocities  will  then  be  as  shown  in  the  following 
table : 


Cyl.  No. 

Feet  per  Second. 

l'  =  M-4-0.60. 

1 

2 
3 

150 
240 
350 

250 
400 
583* 

*  In  the  third  cylinder  the  velocity  will  bs  increased  from  this  value  at  the  first  few 
rows  to  about  900  feet  per  second  at  the  last  rows,  and  -jr  will  decrease  to  about  0.40. 

Let  each  of  the  three  cylinders  absorb  energy  in  the  follow- 
ing proportion: 


Cyl.  No. 

Per  Cent. 

Amount  Absorbed. 

1 
2 
3 

25 
35 
40 

0  25X363=   91  B.T.U. 
0  35X363  =  127      " 
0.40X363  =  145      " 

The  heat  necessary'  to  be  expended  in  each  row  of  blades 
in  order  to  give  the  steam  the  desired  velocity  is  (since 
Vy=22WH.) 

^'  (221)  • 


Cyl.  No. 

H. 

1 
2 
3 

THE   IMPULSE'AND-RE ACTION   TURBINE 


191 


The  number  of  rows,  including  both  movable  and  stationary 
blades,  required  to  absorb  the  available  energy  in  each  stage 
will  then  be: 


Cyl.  No. 

Xo.  of  Rows. 

1 

91 

,   ., .  =  72  +   or  36  in  rotor  and  36  in  casing. 
1.2o                                                                       ^ 

2 

127 

^-^  =  40       or  20  in  rotor  and  20  in  casing. 

3 

145 

^-^  =  21+   or  11  in  rotor  and   11  in  casing. 

If  the  revolutions  per  minute  are  to  be  3600,  or  60  per 
second,  the  mean  diameters  of  cylinders  to  give  the  required 
peripheral  velocity  will  be: 


Cyl.  Xo. 

w. 

Diameter  of  Mean  BIa<le  Circle. 

1 
2 
3 

150 
240 
3.50 

150 

3.14X60     "'^f^--   ^-S'"-     '=aylO". 

240 
3  14X6(J^-^-^^  ^*-^  ^^-"^  in. -say  15}". 

350 

3  14X60     l«<^tt----4in.-say22J  . 

The  cross-sectional  area  of  the  annular  space  occupied  by 
blades,  between  the  rotor  and  the  casing,  is  ordinarily  made 
from  2\  to  3  times  the  net  area  required  for  steam  flow  at  the 
velocity  upon  which  the  design  is  based.  This  is  because  the 
ratio  of  the  area  of  annular  space  to  the  area  of  exit  openings 
between  the  blades,  is  equal  to  from  2.5  to  3.0.  The  blade 
height  depends  upon  this  ratio,  the  volume  of  steam  passing 
per  unit  of  time,  and  the  velocity  of  the  steam  leaving  the 
blatles.     If  the  required  area  at  any  cross-section  is  ^1  square 


192  STEAM-TURBINES. 

inches,  and  if  the  mean  diameter  of  blade-circle  at  that  sec- 
tion is  D  inches,  then 

SA 

Blade  height  =  »  -.  4^  r>  inches. 

Let  it  be  assumed  that  the  steam  consumption  of  the  tur- 
bine at  the  rated  full  load  of  1000  B.H.P.  is  to  be  12  pounds 
per  B.H.P.-hour,  or  that  12,000  pounds  of  steam  are  to  pass 
through  the  blades  per  hour.  This  is  equivalent  to  3.33  pounds 
per  second. 

The  initial  steam  pressure  at  entrance  to  the  blades  of  the 
first  cylinder  is  lower  than  the  throttle-valve  pressure  by  per- 
haps 15  to  25  pounds,  because  of  the  wire-drawing  efTect  of 
the  throttle-valve  movement,  when  acted  upon  by  a  flyball 
governor.* 

Assuming  that  in  the  present  case  the  pressure  at  entrance 
to  the  blades  is  150  pounds  absolute,  and  that  the  steam  during 
its  expansion  through  the  throttle-valve  follows  a  constant  heat 
curve  (that  is,  it  expands  without  loss  of  heat  and  without 
doing  any  work)  the  temperature  will  fall  from  991  to  987 
degrees  absolute.  Since  the  temperature  of  saturated  steam  at 
150  pounds  absolute  pressure  is  819  degrees  absolute,  the  steam 
at  entrance  to  the  blades  is  superheated  by  an  amount  equal  to 
987-819  =  168  degrees. 

From  the  curves  of  specific  volume  of  superheated  steam, 
opposite  page  188,  the  specific  volume  at  entrance  is  3.66  cubic 
feet  per  pound. 

If  adiabatic  expansion  takes  place  until  the  steam  shall 
have  given  up  91  B.T.U.  the  pressure  at  the  end  of  cylinder 
No.  1  will  be  approximately  60  pounds  absolute,  and  the  tem- 
perature 798  degrees  absolute.  The  steam  will  then  be  super- 
heated 45  degrees,  and  its  heat  contents  will  be  1197  B.T.U. 
per  pound.    The  specific  volume  will  be  7.94  cubic  feet. 

*  In  some  types  of  Parsons  turbine  the  valve  is  continually  in  motion 
and  this  wire  drawing  takes  place.  In  others  the  valve  is  either  open  or 
closed,  and  the  pressure  of  the  steam  is  constant  under  a  given  load.  In  the 
example  the  former  type  is  assumed. 


THE  I MPULSE-AND-RE ACTION  TURBINE.  193 

Since  the  velocity  of  steam  in  the  first  cylinder  is  to  be 
250  feet  per  second,  the  necessary  cross-sectional  area  at 
entrance  to  and  exit  from  the  cylinder,  respectively,  will  be 

3.33X7.94    ^^_        .  ^_ 

^^ —  =0.106  sq.  ft.  or  lo.2  sq.  ins. 

•  The  mean  diameter  of  the  blade  circle  is  10  inches  and 
therefore  the  blade  heights  at  entrance  and  exit  of  the  cylinder 
are,  respectively, 

=0.6/2  mches, 


3.14X10 

3X15.2 
3.14X10 


1.45  inches. 


The  heat  contents  at  entrance  to  the  second  cylinder  is 
1197  B.T.U.  per  pound,  and  adiabatic  expansion  is  assumed  to 
take  place  until  127  B.T.U.  have  been  given  up.  The  heat 
contents  will  then  be  1197—127  =  1070  B.T.U.,  and  the  pressure 
after  passing  the  second  cylinder  will  be  10§  pounds  absolute 
(from  the  heat-diagram).  The  quality  will  be  0.92  and  the 
specific  volume  34  cubic  feet  per  pound. 

Assuming  that  the  steam  at  entrance  to  the  second  cylinder 
has  the  same  volume  as  at  exit  from  the  first,  the  cross-sectional 
area  at  entrance  to  the  second  cylinder  (that  is,  at  exit  from 
the  fii-st  row  of  blades  of  that  cylinder)  should  be 

3.33  X  7.94 

^^  ' —  =0.066  sq.  ft.  or  9.5  sq.  ins., 

and  at  exit  from  the  cylinder, 
3.33X34 


400 


=0.283  sq.  ft.  or  41  sq.  ins. 


194  STEAM-TURBINES. 

The  corresponding  blade  heights  at  entrance  and  exit,  re- 
spectively, are  (the  mean  diameter  of  cylinder  being  15.25 
inches) 

3X9.5 

0.595  inches, 


3.14X15.25 

3X41 
3.14X15.25 


=2.57  inches. 


In  similar  manner  the  blade  length  at  entrance  to  the  third 
cylinder  is  found  to  be 

3X33.7       ,  ,^  .     , 

=  1.43  mches. 


3.14X22.5 


The  specific  volume  of  steam  at  exit  from  the  last  row  of  blades 
in  the  turbine  is  2S0  cubic  feet  per  pound,  and  if  the  steam  velo- 
city should  remain  constant  at  583  ft.  per  sec.  during  passage 
thi'ough  the  blade  exits  of  the  last  C3-linder,.  the  length  of  blades 
would  become  inconveniently  great.  In  the  present  case  it 
would  be  about  10  inches.  Such  length  is  avoided  by  increas- 
ing the  exit-angles  of  the  blades  as  the  last  rows  are  ap- 
proached, thus  allowing  the  steam  velocity  to  increase  rapidly, 
and  permitting  the  use  of  shorter  blades.  Thus,  if  the  velocity 
should  be  increased  to  900  feet  per  second,  the  cross-sectional 
area  required  would  be  150  square  inches,  and  the  blade  length 

6.35  inches. 


3.14X22.5 


Summing  up,  such  particulars  as  have  been  determined  for 
the  turbine  would  be  as  follows: 

Delivered  horse-power  at  full  rated  load,  1000. 

Revolutions  per  minute,  3600. 

Nimiber  of  cylinders,  3. 

Initial  steam  pressure  175  pounds  absolute  at  throttle. 

Superheat,  160°  F.  at  throttle. 

Vacuum,  28  inches. 


THE  IMPULSE-AND-RE ACTION  TURBINE. 


195 


Cyl. 

No. 

Mean 
Uiam. 

Blade 
Circle. 

No.  Rows 

on 

Rotor. 

Peri- 
pheral 

Velocity, 
Ft.  per 

Second. 

Steam 

Velocity. 

Ft.  per 

Seconil. 

Heat 
Drop. 
B.T.U. 

Pressure 
at  En- 
trance to 

Cyl.. 
Pds.Abs. 

Blade 
Length  at 
Entrance 

to  Cyl. 
Inches. 

Blade 
Length 
at  E.xit 
from 
Cyl.. 
Inches. 

1 
2 

8 

10" 

l.H" 

22^" 

36 

20 
11 

150 
240 
350 

250 

400 

583  + 

91 

127 
145 

150.0 
60.0 
10.5 

0.67 
0.60 
1.43 

1.45 
2.57 
6.35 

It  will  be  shown  in  the  following  detailed  study  of  the  tur- 
bine, how  velocity  and  volume  of  the  steam  are  affected  by 
frictional  and  other  losses,  and  how  these  affect  the  dimen- 
sions of  the  turbine. 

The  work  done  in  the  first  stationaiy  blades  of  the  fiic- 
tionless  reaction- turbine   is    that  nece&sarv    to  accelerate   the 


Fig.  67. 


jet  from  its  practically  zero  velocity  at  entrance  to  the  turbine- 
casing  to  the  velocity  Vi  at  which  it  enters  the  first  moving 
blades.  If  the  work  in  the  stationary  blades  is  called  Kg, 
then 

^ • 

f  *  Per  pound  of  stpam. 


196 


STEAM-TURBINES. 


The  velocity  relatively  to  the  moving  blades,  at  entrance  to 
them,  is  Vi,  and  this  increases  to  V2  at  exit  from  the  moving 
blades.    The  work  done  in  the  moving  blades  is  then 


Km  = 


Part  of  Kg  produces  pressure  against  the  blades  and  part  is 
lost  as  exit  energy,  due  to  the  velocity  ¥2- 


Fig.  68. 
The  total  work,  including  the  energy  in  the  exit  steam,  is 

Kt  -Ks+Km- 

The  work  done  in  the  moving  blades  is  to  the  total  work  done  as 
-7^,  and  tliis  fraction  is  called  the  "  degree  of  reaction." 
The  net  work  accompHshed  upon  the  turbine  is 


K  =  K,-{-Km-^, 


2g 


expressed  in  foot-pounds,  and  the  efficiency  is 

K-^{K,  +  Km)- 


THE  IMPULSE-AND-RE ACTION  TURBINE.  197 

Example  No.  1. — Let  initial  steam-pressure  =  150  pounds 
per  square  inch  absolute;  let  the  drop  in  pressure  in  the  first 
set  of  guide-blades  be  10  pds.  and  let  a  similar  drop  occur 
in  the  first  set  of  moving  blades.  Let  a'l  =30°  and  let  0-2  =«i- 
Find  the  Avork  done  on  the  moving  blades  per  pd.  steam.  Let 
peripheral  velocity  =  250  ft.  per  second. 

It  is  first  necessary  to  calculate  the  velocity  at  entrance 
to  the  moving  blades.  Assume  the  expansion  to  be  adiabatic, 
with  no  frictional  losses. 


u  =  250  ft.  sec. 
Fig.  69. 

Heat  given  up  in  guide-blades  =  6.0  B.T.U.  or  Fi=550  ft. 
per  second.     From  the  velocity  diagram,  Vx  =360  ft.  per  second. 

The  work   done   in   the   moving   blades  is  — ^ — ^~  foot-pds., 

which  equals  the  heat  given  up  during  the  passage  of  the  steam 
through  the  moving  blades  multiphed  by  778.  The  heat  given 
up  during  adiabatic  expansion  from  140  to  130  pds.  is  6.9  B.T.U. 

Then  ^^^^^^^  =  6.9X778, 

or 


r2  =V64.4X 6.9 X  778  + (360)2 =\/475,312  =  690  f^.  per  sec, 

approximately.    The  work  done  in  the  stationary  blades  is 

Y2     (550)2 
Ks  =  -^  =  ~aT~r  =4700  ft.-pds.  per  sec. 


198  STEAM-TURBINES. 

The  work  done  in  the  moving  blades  is 

,,,2_,^2     (690F- (360)2 
Km=- — «: —  = TTji =5360  it.-pds.  per  sec. 

The  total  work  done  is 

/vi  =  /C+i'w  =  4700 +  5360  =  10,060  ft.-pds.  per  sec. 
From  this  last  is  to  be  deducted  the  work 

?r~=   m  I  =3890  ft.-pds.  per  sec. 
2g       6-1.4  '■        '■ 

The  net  work  accomphshed  in  the  turbine  is 

y,2 

K  =  Kg  +  Km  —  ~^  =6170  ft.-pds.  per  sec, 

or  11.2  horse-power. 

The  efficiency  is 

K      _  6170 
Ks  +  K„,     10,060  /*^' 

The  degree  of  reaction  is 

Kt  "10,060 


=  0.536, 


or  approximately  one-half  degree  reaction,  which  is  about  that 
used  in  reaction-turbine  construction.  The  exhaust  energy  in 
the  above  turbine  is  so  high  that  the  steam  consumption  would 
be  very  large,  and  the  need  for  more  stages  is  obvious.  Thus 
the  steam  consumption  per  horse-power  per  hour  would  be 

r  — „-  =321  pounds  for  a  turbine  of  only  one  stage. 


THE  IMPULSE-AND-REACTION   TURBINE. 


109 


The  many-stage  reaction-turbine  consists  of  guide  and 
rotating  rows  of  blades,  as  indicated  in  Fig.  70.  There  may 
be  many  consecutive  rows,  all  having  the  same  diameter, 
followed  by  others  of  greater  diameter,  as  the  required  area 
for  passage  of  the  steam  becomes  greater  and  greater. 

Assuming  that  the  diameter  of  the  rows,  or  wheels,  is  con» 


stage  A  <^ 


stage  B  < 


Stage  C  < 


It  =250 


Fig.  70. 


stant,  the  peripheral  velocity  of  all  blades  will  be  the  same. 
Let  this  be  called  u,  as  before. 

The  diagram,  Fig.  70,  is  constructed  for  constant  condi- 
tions of  absolute  and  relative  velocity  throughout  the  variou.s 
stages,  and,  as  stated  above,  all  stages  are  alike  in  diameter. 
In  the  first  guide-wheel  the  work  done  is 


Vi^^2g. 


200  STEAM-TURBINES. 

In  the  first  moving  wheel  the  work  done  by  expansion  of  the 
steam  is  that  due  to  increase  of  velocity  from  ri  to  V2  and  ecjuals 


2</     • 

In  each  guide-wheel  after  the  first  the  work  done  is  due  to 
increase  from  V2  to  V[,  and  the  kinetic  energy  thus  produced 
and  then  applied  to  the  succeeding  moving  blades  ecjuals 

7-2_7  2 


2^       ' 

and  the  work  in  each  moving  wheel  is  the  same   as  stated 
above;  that  is, 


v-z-  — 1\^ 


2^      • 

In  general,  if  there  are  ti  sets  of  wheels  (that  is,  n  stagesj ,  each 
consisting  of  one  guide  and  one  moving  wheel,  there  will  be 
??  — 1  sets,  or  stages,  besides  the  first  stage.  The  total  work 
including  that  of  the  first  stage  will  be 


^''V^^-(«-)[(^^)-(^)]- 


2g   '       2g 


Let  /v  =  the  work  in  each  stage  except  the  first,  so  that 

The  efficiency  of  a  single  stage  may  be  found  as  follows: 
If  tt'2  =  ai,  as  in  Figs.  67  and  68,  then  Fi  =  r2,  and  V2  =  V\, 

A  =  2   -— — -    and  erhciencv=A 


2(/     /  Ig  V  1- 

But  from  Fig.  62,  by  trigonometry, 

'c^  =  V2  +  u^-  2uV^  cos  a. 


THE  IMPULSE-AXD-REACTIOX   TURBINE.  201 

Therefore  the  efficiency  =  ■ — „  '     -  77^ 

=  ^[2cosa-^]. 

The  variation  of  efficiency  for   Fi=300  feet  per  second, 
with  variation  of  a  and  u,  is  shown  on  page  228. 
The  total  work  done  in  n  stages  is 

K  +  (;i  - 1) A  +  TT-  =  nK  ^    '  . 
2j  27 

Since  —   is  the  work  lost  at  exit  from   the  turbine,  the  net 

work  done,  per  pound  of  steam,  =?iK. 

Example  No.  2. — Taking  the  velocities  as  given  in  Fig.  70, 

Fi  =  550  for  each  guide-wheel, 
Vo  =  500  for  each  guide-wheel, 
Vi  =  360  for  each  moving  wheel, 
V2  =  690  for  each  moving  wheel, 

„     (550F-(500F   ,  (690)2 -(360?     ^^_^^^     ^ 
A  = ^_Q^ + ^— =  61/0  f t.-pds., 

work  done  in  each  stage  per  pound  of  steam  used.  This  is, 
of  course,  for  a  frictionless  and  otherwise  ideal  turbine.  In 
such  a  machine,  if  expansion  occurred  from  150  pds.  abs.  to 
130  pds.  as  in  the  example  on  page  197,  there  would  be  avail- 
able 12.9  B.T.U.  or,  approximately,  10,000  foot-pounds  of 
energy  per  pound  of  steam,  and  an  ideal  turbine  would  require 

only  p'-^  =1.62  stages  to  completely  utihze  the  energy  avail- 
able. 

If  expansion  should  occur  from  150  pds.  to  1.5  pds.  abso- 
lute, as  in  the  example  on  page  83,  there  would  be  290  B.T.U. 
available,    or    290x778  =  225,000    foot-pounds.     In    an    ideal 


202  STEAM-TURBINES. 

reaction-turbine  of  the  kind  above  descr.bed,  the  number  of 
stages  required  to  absorb  this  energy  would  be 

225,000 
^.„^    =  36,  approxnnately. 

Action  of  the  Steam  upon  the  Buckets. — The  guide-blades 
act  as  nozzles  leading  to  the  moving- blades.  Under  normal 
conditions  the  guide-blades  receive  steam  from  the  preceding 
moving-blades  at  an  absolute  velocity,  or  velocity  with  respect 
to  the  earth,  of  V2  (Fig.  68),  and  discharge  it  upon  the  suc- 
ceeding moving- blades  at  velocity  Vi,  larger  than  V2.  Con- 
sidered with  respect  to  the  motion  of  the  moving-blades,  the 
velocity  of  the  entering  steam  is  vi,  and  during  its  passage 
through  the  moving-blades  the  steam  has  its  velocity  relatively 
to  the  moving-blades  increased  to  Vo.  The  total  work  done 
upon  the  row  of  moving-blades  is  that  due  to  the  following 
two  causes:  First,  impulse,  as  the  energy  {Vi^ —  V'^)  -^2g  per 
pound  of  steam,  produced  in  the  guide-blades,  is  expended 
upon  the  moving-blades;  and,  second,  the  reaction  accom- 
panying the  change  in  the  moving-blades  from  vi  to  V2, 
and  resulting  in  an  energy  expenditure  upon  the  blades  of 
{V'^  —Vi^)  ^2g  per  pound  of  steam  used.  The  guide-  and 
moving-blades  are  ordinarily  approximately  alike  as  to  angles, 
and  when  this  is  so,  half  the  work  is  due  to  impulse  and  half 
to  reaction,  provided  that  the  heat-drop  is  the  same  in  the 
two  rows.  If  V2  should  equal  Vi,  as  in  Fig.  71,  the  work 
would  be  due  entirely  to  reaction,  and  equal  to  {v-^  —  vr)  -^  2g. 
If  V2  should  equal  Vi,  the  total  work  would  be  due  to  impulse, 
and  equal  to  (Fi^  — F2'-) -^2.7,  just  as  in  the  impulse- turbine. 
If  V2'  should  equal  vi,  and  F2"  =  Fi,  as  shown  in  dotted  lines, 
the  l^lade  would  no  longer  be  curved,  but  would  have  the  out- 
line AB  (Fig.  71)  and  the  work  done  would  be  zero. 

Losses  of  Energy  in  the  Turbine  may  be  classified  as  follows : 

(a)  The  effect  of  friction  between  the  steam  and  the  metallic 

walls  and  moving  parts  of  the  turbine,  which  is  to  cause  the 

exhaust    from  a  given  stage  to  carry  away  more  heat-energy 


THE  IMP ULSE-ANB-RE ACTION  TURBINE. 


203 


than  it  would  in  a  frictionless  conducting-channel.     The  cause 
of  this  is  described  in  Chapter  V.    A  similar  result  is  brought 


Fig.  71. 

about  by  the  friction  due  to  eddies  in  the  steam.  The  "curve 
of  frictional  effect"  (page  219).  is  useful  in  representing  the 
variation  of  this  source  of  loss,  but  it  is  by  no  means  certain 
that  the  friction  loss  varies  according  to  the  curve  in  Fig.  77. 
Examples  4  and  5  assume  the  loss  to  be  constant,  correspond- 
ing to  a  value  of  i/  =  0.28. 

(6)  Resistance  to  movement  of  the  rotating  parts  in  the 
atmosphere  of  steam  within  the  turbine  casing,  called  "wind- 
age." Tliis  causes  a  frictional  loss,  and  its  effect  is  probably 
greatest  at  the  high-pressure  end  of  the  turbine,  cUminishing 
as  the  low-pressure  end  is  approached. 

(c)  Mechanical  friction  in  journal-bearings,  glands,  and 
stuffing-boxes. 

id)  Leakage  losses  through  clearance- spaces,  glands,  etc. 

(e)  Radiation  losses. 

The  steam  consumption  of  a  turbine  working  between  known 
limits  may  be  calculated  as  follows,  for  assumed  losses  due  to 
steam  friction  and  friction  of  rotating  parts,  and  loss  due  to 
leakage.  The  dotted  Une,  Fig.  72,  indicates  the  condition  of  the 
steam  during  expansion  through  the  turbine. 


a  w 


a 

5^ 

< 

0? 

t^ 

S3 

iJ 

n 

Xi 

H 

H 

3 

K 

H 

fS 

« 

[>4 

g 

o 

^ 

g 

V 

-5 

-tJ 

•S 

n 

CQ 

h 

n 

tc 

o 

p 

iJ 

M 

c 

^g 

g 

o 

2  c« 

-2  « 

K  2 

-*3 

E- 

m 

P3 

s 

J< 

p 

< 

204 


THE  IMPULSE-AND-REACTION  TURBINE.  205 

First,  assuiniiig  adiabatic  expansion,  allowing  for  no  losses: 

Heat  of  liquid     at  165  pds.  abs.  .  .=   337.6  337.6 

Heat  of  vapor'n  at  165    "      "    ..=   855.3     855.3   X  0.98    =838.2 


Heat  of  liquid    at  1.23  pds.  abs.  .  .  =  77.06 

Heat  of  vapor'n  at  1.23  "      "    ..  =  1037.8 

1037.8X0.763  =  791.84 


1175.8 


868.90         868.90 


Heat  given  up  =  Hi-H2= T  .  .   306.9  B.T.U. 

Let  the  loss  of  heat  in  the  blades,  due  to  friction,  correspond 
to  y  =  .2Q,  or  (l-2/)(i/i -^2)  =306.9X0.74  =  227  B.T.U.  Sup- 
pose the  energy  in  the  exhaust  is  4%  of  the  initial  energy 


E  =  .u'Jas 


lG5.pds.^j  ^  =.5223  +.98  X  1.035  =  1.5 
1(  quality  =  .98) 


E=.1453 


E  =  1.391 


E  =  1.821 


quality  =.T634-BlilM?  =  .836 
1038 

E  =  1.967        T2=  569.8°ab». 

Po=  2,5  inches  mere. 
=  1,23  pds.  abs. 
JE=  1.536 

(quality  =-f||i=  ,^63 


Fig.  72. 


minus  loss  in  the  blades,  and  the  loss  due  to  friction  of  the 
rotating  drum  and  of  the  bearings  =  14%.  Let  the  loss  due 
to  leakage  =7%.  Sum  of  losses  =  25%,  besides  the  26%  heat 
loss  due  to  steam  friction.  Then  75%  X  227  =  170  B.T.U. 
available  from  each  pound  of  steam  flowing  through  the  tur- 
bine. Suppose  1  pd.  flows  per  sec,  or  3600  pds.  per  hour. 
Ft.-pds.  per  min.=  60X170x778  =  7,935,600.      Horse-power  = 

7,935,600    ^.^      ^^  ,.         3600 

--—-—-=240.     Steam  consumption  = -xr^r- =  15  pds.  per  de- 

00,000  ^"±0 

livered  horse-power  hour. 


206  STEAM-TURBINES. 

In  reaction-turbine  design  the  assumptions  made  at  the  start 
are  chosen  from  among  the  following  items : 

1.  Initial  and  final  steam-pressures. 

2.  Initial  quality  of  steam,  or  degree  of  superheat,  if  any. 

3.  Losses  to  be  experienced  by  the  steam  during  its  passage 
through  the  machine. 

4.  Initial  velocity  of  steam  as  it  leaves  the  guitle-blades. 

5.  Angle  at  which  the  guide-blades  discharge  to  the  moving 
blades. 

6.  Angle  at  which  the  moving  blades  discharge  to  the 
guide-blades. 

7.  Peripheral  velocity  of  the  blades  in  the  various  cylinders. 

Assumptions  as  to  the  above  make  it  possible  to  deter- 
mine cross-sectional  areas  at  different  points  in  the  turbine, 
the  length  and  width  of  blades,  and  to  estimate  the  heat  losses. 
From  these  data  the  probable  steam  consumption  may  be 
calculated  for  a  given  rate  of  power  developed. 

The  number  of  revolutions  per  minute  may  be  decided 
upon  from  considerations  of  the  use  for  which  the  turbine  is 
intended.  The  drop  in  energy  in  the  various  stages  deter- 
mines the  initial  velocity  of  steam  through  the  blades,  and 
the  peripheral  velocity  of  the  latter  is  usually  from  one  third  to 
two  thirds  or  more  of  the  steam  velocity,  the  ratio  for  highest 
efR2iency  depending  upon  the  exit  angles  of  the  blades.* 

From  Fig.  73  it  is  obvious  that  the  cross-sectional  area 
through  a  row  of  blades  decreases  as  the  exit  angle  with  the 
direction  of  motion  of  the  blade  becomes  smaller.  Considering 
the  two  extreme  limiting  cases,  if  the  steam  were  discharged 
from  a  set  of  blades  in  the  direction  of  motion  of  the  blades — 
that  is,  if  a  became  zero — the  cross-sectional  area  would  become 
zero.  If  the  blades  discharged  in  an  axial  direction,  the  cross- 
sectional  area,  assuming  infinitely  thin  blades,  would  be  equal 
to  the  length  of  the  blades,  multiplied  by  the  circumference 
on  the  mean  diameter  of  the  row  of  blades.  That  is,  the  area 
would   equal   the   whole   annular   area   swept    by   the   blades. 

lu  electrical  work  a  ratio  of  about  0-6  Las  beeu  frequently  used.      See 
page  226  for  further  data. 


THE   IMPULSE-AND-REACTION  TURBINE. 


207 


208  STEAM-TURBINES 

Between  these  two  extremes  are  the  actual  conditions,  and 
the  actual  area  for  infinitely  thin  blades  would  be  to  the  whole 
annular  area  swept  by  the  blades  as  a  is  to  h  (Fig.  73).  But 
a-^h  =  sina,  and  the  area  for  blades  having  a  length  L  and 
rotating  on  a  mean  diameter  D  would  be 

area  =  7:DL  sin  a. 

The  blades  have  a  certain  thickness  to  afford  strength,  and 
the  diameter  of  cylinder  and  length  of  blades  must  be  propor- 
tioned so  that  the  required  area  for  passage  of  steam  may  be 
obtained.  If  the  thickness  of  the  blades  is  half  the  mean 
clear  opening  between  two  blades,  then  the  area  correspond- 
ing to  blades  without  thickness  should  be  multiplied  by  1.5, 
and  the  proper  diameter  of  cyHnder  and  length  of  blades  cal- 
culated. The  blade  thickness  must  in  all  cases  be  taken 
account  of  in  calculating  cross-sectional  area. 

Fig.  73  shows  how  the  area  decreases  with  the  angle  a, 
and  that  for  a  given  axial  space  occupied  by  a  row  of  blades 
the  steam-channel  becomes  longer,  as  well  as  narrower,  with 
decrease  of  the  angle  a.  From  these  facts  it  follows  that, 
while  the  power  absorbed  per  stage  apparently  increases  as  a 
decreases,  thus  reducing  the  number  of  stages,  the  friction 
losses  become  greater  as  a  decreases.  There  is  thus  a  Hmit 
beyond  which  it  does  not  pay  to  decrease  the  exit  angles.  In 
reaction-turbines  the  exit  angle  is  ordinarily  from  20°  to  30° 
for  both  guide  and  moving  blades.  If  the  exit  angle  is  made 
too  large,  each  stage  absorbs  and  dehvers  too  Uttle  energy, 
and  too  many  stages  are  required.  This  not  only  increases 
the  size  of  the  turbine,  but  also  lengthens  the  path  of  the  steam 
and  makes  the  friction  losses  greater. 

It  has  been  shown  that  the  friction  losses  increase  with 
the  square  of  the  velocity  of  the  steam.  Making  the  drop  in 
each  wheel  small,  by  increasing  the  exit  angles,  results  in 
increa'^ed  number  of  stages,  and  large  friction  losses,  due  to 
the  lengthened  steam  path.  Making  the  drop  large  in  each 
stage  increases  the  velocity  of  steam,  and  the  friction  losses 
increase  as  the  square  of  the  velocity.    The  choice  of  the  con- 


THE  IMPULSE-AND-REACTION   TURBINE.  209 

ditions  as  outlined  at  the  top  of  page  206  is  to  be  made  with 
a  view  to  reducing  friction  and  other  losses  to  a  minimum, 
by  properly  proportioning,  with  respect  to  each  other,  the 
peripheral  velocity  of  the  blades  of  the  various  stages,  the 
angles  of  exit,  and  the  drop  in  heat  contents  per  stage,  which 
determines  the  velocity  of  the  steam. 

In  making  calculations  based  on  the  preliminary  assum- 
tions,  the  heat  diagram  is  used.  Considering  only  that  por- 
tion to  the  left  of  the  curve  of  saturated  steam,  curves  of 
constant  heat,  constant  quality,  and  constant  volume  are 
drawn,  and  methods  of  interpolation  may  be  used  for  finding 
the  quality,  volume,  and  heat  contents  of  steam  at  any  tem- 
perature and  specific  entropy  wdthin  the  Hmits  of  the  dia- 
gram. 

The  intervals  between  all  quality  curves  are  ahke  for  any 
one  temperature,  and  the  same  is  true  of  the  curves  of  con- 
stant heat. 

Example  No.  4- — Let  steam  at  165  pds.  abs.  and  98% 
quality  expand  to  a  pressure  of  2.5  inches  of  mercury,  or  1.23 
pds.  abs.  The  upper  and  lower  temperatures  are  826.5  and 
570  degrees  absolute  respectively. 

(a)  Assuming  that  expansion  is  not  adiabatic,  but  that  the 
steam  loses  26%  because  of  friction,  find  what  the  quality  of 
the  steam  will  be  at  the  lower  temperature,  and  at  600,  650, 
700,  750,  and  800  degrees  absolute.  See  dotted  expansion  line, 
Fig.  72.    Note  also  Fig.  26  and  discussion  in  Chap.  V. 

(6)  Find  the  heat  contents,  per  pound  of  the  steam,  at  each 
of  the  above  temperatures. 

(c)  Plot  curves  of  heat  drop,  and  of  specific  volume  of  the 
steam,  for  the  expansion  indicated,  as  is  done  on  page  211. 
To  find  the  volumes,  multiply  the  specific  volume  of  dry  steam 
at  the  various  temperatures  by  the  corresponding  quaUties. 

By  plotting  an  expansion  curve  on  the  heat  diagram  using 
the  qualities  found  in  (a)  the  curve  of  "  heat-given-up  "  may 
at  once  be  derived.  Use  of  the  tabular  form  given  on  p.  202 
will  greatly  simplify  and  facilitate  calculation. 


210  STEAM-TURBINES 

The  curves  asked  for  in  the  above  example,  and  plotted  in 
Fig.  74,  represent  the  characteristics  of  the  turbine,  giving 
for  each  cyhnder  the  mean  values  of  peripheral  and  steam 
velocity,  and  mean  cross-sectional  areas  for  passage  of  steam. 
These  are  tabulated  below.  In  designing  it  is  advisable  ta 
plot  the  curves  as  the  first  step,  and  calculate  the  remaining 
quantities  in  the  table  from  the  curves  as  a  basis. 

Let  the  peripheral  velocity  of  the  turbine-blades  vary  as 
shown  on  the  curve  (Fig.  74),  and  let  the  relation  between 
peripheral  and  steam  velocities  at  entrance  to  the  moving 
blades  be  as  follows : 

u 

Tr=0.35. 
Vi 

From  this  and  the  curve  of  peripheral  velocity  the  curve  of  Vi 
may  be  plotted.  The  curve  of  peripheral  velocity  is  assumed 
so  that  a  satisfactory  length  may  be  given  the  turbine-blades. 
The  blades  of  the  first  cyhnder  should  not  be  excessively  short, 
otherwise  the  clearance  would  be  too  great  a  percentage  of 
the  total  cross-sectional  area.  A  high  peripheral  velocity 
means  high  initial  steam  velocity,  w^hich  in  turn  means  small 
cross-sectional  area  for  passage  of  steam,  and  consequently 
short  blades.  A  certain  amount  of  clearance  space  is  necessary 
for  mechanical  reasons,  and  steam  is  free  to  leak  through  with- 
out doing  work.  If  the  blades  are  very  short,  the  clearance 
becomes  a  considerable  percentage  of  the  total  cross-sectional 
area  for  passage  of  steam,  and  leakage  is  excessive.  For  this 
reason  the  initial  peripheral  and  steam  velocities  are  kept 
low  and  the  blades  made  correspondingly  long. 

From  these  considerations  the  curve  of  peripheral  velocity 
begins  at  about  130  ft.  per  second  in  the  present  case  and 
gradually  increases  to  about  350  ft.  per  second.  The  cor- 
responding initial  steam  velocity  curve  begins  at  360  and 
ends  at  about  1040  ft.  per  second,  between  the  Hmits  of  tem- 
perature 826  and  570  degrees  absolute.  The  relation  between 
these  two  curves  is  Fi  =  1^^0.35. 


THE  IMPULSE-AND-REACTION   TURBINE. 


211 


850 

800 

750 

Abs.  Temp. 
700 

G50 

CO-) 

j 

550 

/ 

/— 

/ 

•iOU 

120 

/ 

/ 

300 

/ 

1  j 

d 
'-'    80 

^ 

y 

i/ 

150 

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y 

/ 

40 

V\v 

^ 

/ 

100 

SP' 

Vio 

laV 

.vv>- 

t^ 

/ 

/ 

^ 

y 

0 

50 

. 

^ 

Sp, 

Vo 

h± 

-inr 

g  j 

/ill 

1 

— ■ 

" 

0 

240 

1200 

220 

' 

llOO 

/ 

^0 

/ 

/ 

* 

1000 

/ 

1 

/ 

180 

/ 

/ 

900 

^\/ 

160 

/ 

/■/.' 

800 

/ 

/ 

^140 

f4 

^y 

/^ 

^' 

700 

.^y 

/, 

c> 

180 

4 

^ 

COO 

^ 

y. 

A 

*' 

(0 

<^ 

y 

500 

^ 

? 

80 

■^ 

/ 

400 

_ 



— 

' 

/ 

y 

60 

/ 

^ 

y 

300 

/ 

AiJ 

^ 

^ 

40 

/ 

jiv 

^ 

.vi^ 

200 

/ 

A 

8SU 

jnee 

--^ 

^ 

lO 

20 

■ 

— 

— 

7^ 

■■= 

o 

100 

^ 

/ 

85 

0 

o 

80 

0 

c 

75 

0 

c 
At 

Fi 

7C 
G 

0 
reir 

74 

p- 

K 

0 

( 

m 

p 

55 

0 

212 


STEAM-TURBINES. 


Let  the  turbine  consist  of  five  cylinders,  the  blades  being  of 
a  single  length  for  each  cylinder.  The  cylinders  will  be  arranged 
to  absorb  the  heat  drop  between  the  temperature  lines  shown 
in  Fig.  74,  and  in  the  following  table,  which  contains  various 
necessary  quantities  taken  from  the  curves,  or  calculated  as 
described : 


Mean 

Average 

Mean 

Mean 
Initial 

Mean 

Diameter 

Cross- 

Length 

•Cylinder 

No 

Degrees 
Temp. 

B.T.  U. 

Heat 

Periph- 

Sp.  Vol. 
of 

of  Row 

of 

sectional 
Area  of 

of 
Blades, 

Drop. 

Drop. 

Vel.  u. 

Steam. 

Blades, 
Ins. 

Cylinder, 
Sq.  In. 

Ins. 

1 

56 

43 

130 

375 

4.03 

16.5 

6.5 

.50 

2 

60 

53 

150 

420 

9.02 

19.0 

13.0 

.875 

3 

60 

53 

200 

550 

24.80 

25.5 

27.3 

1.37 

4 

45 

46 

270 

750 

66.80 

34.5 

53.8 

2.00 

5 

35 

32 

330 

950 

164.00 

42.0 

103.0 

3.14 

Let  the  turbine  be  required  to  develop  1000  brake  horse- 
power, at  1800  revolutions  per  minute  or  30  per  second.  This 
fixes  the  mean  cUameter  of  the  rows  of  blades  of  the  various 
^yhnders,  since  the  peripheral  velocity  is  determined  by  the 
curve.  Let  this  be  calculated  and  inserted  in  the  table  as 
above.  The  mean  specific  volume  of  the  mixture  of  «team 
and  water  may  be  found  from  the  curve  at  the  top  of  Fig.  74, 
for  each  cylinder.  The  curve  is  to  be  found,  in  the  first  place, 
from  the  steam-table  values  of  specific  volume  of  dry  steam, 
by  multiplying  these  by  the  quality  of  steam  as  determined 
from  the  expansion  curve  on  the  diagram.  Each  cylinder 
of  a  turbine  is  usually  made  to  gradually  enlarge  in  cross- 
sectional  area  as  the  steam  expands.  The  present  calcula- 
tions apply  to  the  average  cross-section  for  each  cylinder. 

To  find  the  cross-sectional  areas  it  is  necessary  to  cal- 
culate or  to  ascertain  in  some  way  the  probable  steam  con- 
sumption of  the  turbine,  as  the  volume  of  steam  flowing  per 
second  is  required.  From  the  expan.sion  curve  on  the  heat 
diag.fam,  the  heat  given  up  per  pound  of  steam  may  be  found 
by  measurement.  In  this  case  it  is  the  same  as  the  quantity 
found  on  page  205,  or  227  B.T.U.    Let  the  other  losses  be  the 


THE  IMPULSE-AND-REACTiON   TURBINE.  213 

same  as  found  on  page  205,  which  result  in  a  steam  consumption 
of  15  pounds  per  brake  horse-power  hour. 

To  calculate  the  cross-sectional  area  for  each  cyhnder  let 
v  =  mean  specific  volume  of  the  steam  and  water  mixture  at. 
the    cyhnder    under    consideration.    The   weight    flowing   per 

second  when  developing  1000  horse-power  will  be    .,'    ,.  =4.2 

pounds,  and  the  volume  per  second  will  be  4.2  XV.  Taking 
the  velocity  as  that  at  exit  from  the  guide-blades,  the  cross- 
sectional  areas  for  the  first  and  the  succeechng  cyhnders  vn]l  be  I 

.      4.2X4.03    ^^^.        .^         _        . 
Ai= — 7;z^ — =0.04o  sq.  tt.=     o.o  so.  nis. 
6to 


A2=   '    .^^'  ^  =  0.090  "    ''=   13.0 


A 


4.2X9.02 
420 

4.2X24.8 


550 


/oO 

4  2  V  1  fi4 
A^  =  — ^--^  =  0.715  "    ''=103.0''     " 
9o0 

These  are  inserted  in  the  table  above. 

To  find  the  length  of  blades  in  the  present  problem  assume- 
that  the  exit  angle  for  all  the  stages  is  22  degrees. 

As  shown  on  page  208,  if  L  is  the  length  of  blade,  and  D 
the  mean  diameter  of  section  of  the  annular  space  occupied 
by  blades,  the  net  area  for  passage  of  steam  would  be,  for 
infinitely  thin  blades, 

A=7rDLsina,     or    L=  ^^—^ . 

-D  sm  a 

If  the  blades,  due  to  their  thickness,  occupy  one  third  of  the 
cross-sectional  space,  the  necessary  area  becomes  1.5-4,  or^ 
since  sin  22°  =  0.374, 

1.5.4  1.2SA 

3.14i)x  0.374  ~    D    ' 


214  STEAM-TURBINES. 

Calculating  the  mean  length  of  blade,  the  follo'^'ing  values 
are  obtained: 

^      1.28X6.5      ^.^    .     , 
Li  =  — TTT-^ —    =0.50   inch. 
Ib.o 


1.2SX13 

19 
1.28X27.3 

25.5 
1.2SX53.8 

34.5 

1.23^103 

42 


1/2=— ^7^ —     =0.875 


=  1.37 


L4=   '   „.  .   '   =2.00 


L^  =  - — ^ =3.14 


These  have  been  inserted  in  the  table  on  page  212. 

It  now  remains  to  determine  the  number  of  stages  that  are 
necessary  in  each  cyhnder  to  absorb  the  energy  given  up 
during  the  fall  in  temperature  assumed  at  the  beginning  of 
the  problem. 

From  Fig.  75,  Plate  XIII,  it  is  evident  that  if  0:1=0:2,  Vu 
and  V2a  will  be  equal  to  each  other.    Also,  Via  will  equal  V2a- 

The  energy  given  up  per  stage  in  any  cylinder  is  equal  to 
the  sum  of  the  amounts  given  up  in  a  row  of  guide-blades  and 
a  row  of  moving  blades  and  equals,  for  each  stage  of  the  first 
cyhnder  in  the  present  example, 

But  Via~=V2a^ 

and  V2a^=Via^. 

2(F,„2_r,„2)     2(F,„2_F2«2) 


Therefore  K 


23  2g 


This  s'mply  means  that,  under  the  stated    conditions  (equal 
exit  angles),  the  energy  given  up  in  a  rotating  wheel  equals 


tge 


eo- 


y 


PLATE  XIII. 


Viu=  Absolute   Velocity   Leaving  Guide   Blades,  Stage  a 

Z\.^=  Relative             "              *'               *•              "  "       « 

Vart=  Absolute           "             "         Moving       ••  •■       a 

rju=  Relative            <•            "              ..             •■  "      a 
Similar   Notation   for    Stages  b,  c,  d,    and   e 


THE  IMPULSE-AND-RE ACTION   TURBINE.  215 

that  given  up  in  the  guide-wheel  before  it.  It  is  necessary 
to  construct  the  velocity  diagram  for  only  one  of  the  wheels 
or  rows  of  blades  in  a  cylintler,  since  that  for  the  others  would 
be  exactly  similar. 

In  Plate  XIII  the  single  hne  making  the  angle  a  =22°  with 
the  direction  of  motion  of  the  blades  may  be  used  to  represent 
in  direction  all  the  initial  velocities,  and  combining  them  with 
their  respective  peripheral  velocities  gives  the  relative  veloci- 
ties necessary  for  finding  the  value  of  K  in  the  above  equa- 
tion. The  values  of  T^i  and  V2  tabulated  on  page  212  were 
taken  from  the  velocity  diagram  on  Plate  XIII.  The  work 
done  in  each  stage  of  each  cyhnder,  and  the  number  of  stages 
required  to  absorb  the  energy  given  up  in  each  cylinder,  may 
be  calculated  as  follows:  Taking  the  first  cylinder,  each  stage 
absorbs  the  work 


2(F^/-F2a2)      2[(375)2- (260)2] 
Ka  = 2g ^ 64l ^  ^^^^  f  t.-pds. 

or  2.91  B.T.U. 


Since  there  are  42  B.T.U.  to  be  absorbed  during  the  passage 
of  the  steam  through  this  cyhnder,  the  number  of  stages  re- 
quired will  be 

42 

^  =  14.5, — say  15  stages. 

Similar  calculations  give  the  following  number  of  stages  for 
each  cyhnder. 

No.  of  Stage.  Stages. 

1 15 

2 14 

3 8 

4 , 4 

5 2 


216  STEAM-TURBINES. 

These  figures,  as  they  stand,  would  not  be  satisfactory  for  use 
in  determining  the  final  dimensions  of  a  turbine.  The  angles 
of  the  blades  would  be  varied  more  or  less  from  one  cylinder 
of  blades  to  another,  to  suit  various  requirements,  and  the 
cylinders  would  usually  not  be  so  numerous  as  here  indicated. 
For  a  turbine  of  the  size  given,  three  cyUnders  might  be  used, 
leaving  the  first  two  about  as  the  figures  indicate,  but  rear- 
ranging the  last  three  cyhnders  so  as  to  combine  them  into 
one,  consisting  of  blades  increasing  in  size  as  they  approach 
the  exliaust  end.  By  a  series  of  calculations  similar  to  those 
above,  the  required  variations  may  be  determined. 

The  pressure  drops  in  the  above  example  are,  approximately: 

1st  cylinder 165  pds.  abs.  to  76  pds.  abs. 

2d         "       76    ''     "     "   29    ''     '' 

3d         "       29    "     "     "     9     "     " 

4th       ''       9    "     "     "  3.2    "     " 

5th       ''       3.2    "     "     "  1.2    "     " 

This  large  number  of  cylinders  was  adopted  in  order  to  give 
practice  in  making  the  calculations,  but  a  better  arrangement 
from  both  thermal  and  mechanical  considerations,  would 
result  from  the  following  conditions: 

Example  No.  5. — Proportion  an  impulse-and-reaction  turbine 
according  to  the  curves  given  in  Fig.  74  with  the  following 
pressure  drops: 

Cylinder  No.  Pressure  Drop. 

1. ......  .  165  pds.  abs.  to  50     pds.  abs. 

2 50    ''      ''     ''    16      ''      '' 

3 16    ''     ''     ''      1.2   ''      " 

The  following  table  gives  the  particulars  taken  from  the 
curves  on  page  211.  In  everything  except  pressure  drop  the 
particulars  of  the  design  are  the  same  as  for  the  turbine  of  five 
cylinders,  worked  out  above.  From  the  curves,  page  211, 
and  the  temperature  drop  corresponding  to  the  fall  in   pres- 


THE  IMPULSE-AND-REACTION    TURBINE. 


217 


sure,  the  quantities  are  calculated  as  was  done  in  the  previous 
example. 


Cylin- 

Pres- 
sure 
Drop, 
Pds. 

Tem- 
pera- 
ture 
Drop, 
Degs. 

Heat 
Drop, 
B.T.U. 

Mean  Velocities. 

Mean 

Mean 
Diam- 
eter 
Blades, 
Ins. 

Mean 
Clear 
Area, 
Sq.  In. 

Mean 
I,en'th 
Blades 

Ins. 

Num- 

der 
No. 

Peri- 
pheral. 

Steam 

Steam 

V2. 

Specific 
Volume 
Cu.  Ft. 

ber  of 
Stages 

1 
2 
3 

115. 
34 

14.8 

84 

65 

107 

68 

59 

100 

138 

170 
265 

385 
435 

775 

260 
325 
535 

6 

18 

100 

17.5 
20.5 
34.0 

9.4 
22.7 

78.0 

0.69 
1.42 
2.94 

21 

18 
8 

Each  of  the  sections  of  the  turbine  (three  in  this  case)  is 
properly  called  a  cylinder,  and  each  cylinder  contains  blades 
of  various  lengths,  increasing  as  the  pressure  becomes  lower, 
thus  affording  increasing  area  for  the  passage  of  steam.  Each 
cylinder  may  contain  several  rows  of  blades  of  given  length 
and  contour,  and  then  several  rows  of  another  length  and 
contour.  Each  of  these  sets  of  rows  is  called  a  barrel,  and  a 
cylinder  may  contain  many  barrels.  The  figures  in  the  table 
refer  to  the  mean  dimensions  of  the  respective  cylinders,  hence 
the  blades  at  the  high-pressure  end  of  the  cylinder  will  be 
shorter  and  those  at  the  low-pressure  end  longer  than  given 
in  the  table. 

The  diameter  of  the  spindle,  or  rotating  part  of  the  tur- 
bine, depends  primarily  upon  the  peripheral  velocity  of  blades 
and  the  rate  of  revolution;  the  former  depends  upon  the  initial 
steam  velocity  employed.  With  given  diameters  for  the 
various  cyhnders,  and  with  certain  thickness,  spacing,  and 
exit  angles  of  blatles,  the  length  of  blades  depends  upon  the 
necessary  cross-sectional  area  for  the  passage  of  steam  through 
the  various  cyhnders. 

The  Parsons  type  of  turbine  for  stationary  use  has  ordinarily 
three  cyhnders,  and  the  mean  diameters  of  the  rows  of  blades 
in  the  various  cylinders  are  made  in  about  the  following  pro- 
portion: 

(i  =  mean  diameter  of  smallest  cyHnder; 
1.4  to  1.5d  =    "  "         "  middle  " 

2  to  2.75d=    "  "        "  large  '' 


218  STEAM-TURBINES. 

Calling  one  stationary  and  one  moving  row  of  blades,  taken 
together,  a  stage,  there  are  ordinarily  from  50  to  100  or  more 
stages  in  turbines  of  fairly  large  size;  that  is,  from  300  K.  W. 
upward. 

Since  turbines  are  used  in  connection  with  very  low  exhaust- 
pressures,  the  volume  of  steam  pavssing  the  low-pressure  blades 
per  second  becomes  very  great,  and  the  diameter  and  blade 
dimensions  for  that  end  of  the  machine  should  be  considered 
first.  The  dimensions  of  the  smaller  parts  may  then  be  pro- 
portioned accordingly. 

Variation  of  Friction  Loss. — The  experimental  work  discussed 
in  Chapter  VI  indicates  that  the  friction  losses  in  an  expanding 
nozzle  increase  as  the  pressure  decreases,  and  that  the  increase 
of  the  value  of  y  is  very  rapid  at  very  low  pressures.  Experi- 
ments with  turbines  show  that  much  more  energy  is  lost  if 
the  steam  used  is  moist  than  is  lost  when  dry  or  when  super- 
heated steam  is  used.  During  expansion  the  steam  gives  up 
heat,  as  work,  and  a  considerable  amount  of  water  of  con- 
densation is  formed.  The  presence  of  water  in  the  steam  is 
thought  to  be  responsible  for  what  cutting  of  the  blades  occurs, 
and  this  indicates  that  the  water  causes  resistance  to  passage 
of  the  steam. 

From  these  indications  it  has  sometimes  been  considered 
that  the  friction  loss,  as  represented  by  y,  is  greater  in  extent 
towards  the  low-pressure  end  of  the  machine  than  it  is  at 
early  points  of  the  steam-path,  and  the  "  Curve  of  frictional 
effect  "  shown  in  Fig.  77  has  been  drawn  with  this  point 
in  mind.  It  shows  the  value  of  y  to  be  used  at  each  of  the 
temperatures  dealt  with  in  designing  the  turbine.  The  flatten- 
ing out  of  the  "  Curve  of  heat  given  up  "  shows  that  if  the 
losses  due  to  the  accumulation  of  water  on  the  blades,  or  along 
the  steam-path,  should  increase  according  to  the  curve  assumed, 
it  would  not  pay  to  reduce  the  temperature  of  the  exliaust 
below  540°.  As  the  use  of  superheated  steam  reduces  the 
losses  in  the  turbine,  it  seems  that  a  low  vacuum  is  more 
effective,    economically,    with    superheated    than    with   moist 


THE  IMPULSE-AND-REACTION   TURBINE. 


219 


steam,  although  it  undoubtedly  is  one  of  the  chief  considera- 
tions in  both  cases. 

The   following   problem   involves   some   considerations   not 


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260 

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130 

IGO 

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S  100 
80 
CO 
40 
20 


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Cu 
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Act 
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nl2ij 

table 

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— 

V 

/ 

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_Heat  given  up  during  actu 
corresponding  to  curve  of 

lie 
flic 

<pansi 
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on 

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t. 

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3le 

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r 

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1 

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850 


750  rOO  (J50  600 

-A.l)solute  Temp.,  Deg.  F, 

Fig.   77. 


500 


700 
000 
500 
400 
:300 
200 
100 
0 


taken  up  in  the  foregoing  examples,  and  the  results  correspond 
more  nearly  with  the  proportions  adopted  in  practice.     The 
curves  and  diagrams  in  Figs.  77  and  78  apply  to  this  example. 
Example  No.   6. — Let   a   turbine   be  required   to  develop 


220  STEAM-TURBINES. 

1000  horse-power  at  full  load,  and  be  capable  of  using  suffi- 
cient steam  to  produce  1500  horse-power,  without  the  use 
of  by-pass  valves. 

Let  the  initial  pressure,  at  the  throttle-valve,  be  160  pounds 
absolute  per  square  inch,  and  let  the  condenser  maintain  a 
vacuum  of  29  inches  of  mercury.  The  upper  and  lower  tem- 
peratures will  then  be  824°  and  540°  absolute  respectively. 
The  steam  entering  the  turbine  will  be  supposed  to  be  dry 
and  saturated. 

Let  the  loss  of  energy  due  to  friction  of  bearings,  to  exhaust 
velocity,  and  to  windage  be  18  per  cent  of  the  energy  given  up 
by  the  steam.  The  total  heat  given  up  by  the  steam,  accord- 
ing to  the  curve  in  Fig.  77  is  245  B.T.U.  per  pound,  and  of 
this  82%  is  to  be  useful  in  developing  energy  of  rotation.  The 
steam  consumption  of  the  turbine  will  then  be 

1,980,000  ,^^  ,  ,  r         lu  u 

TT-^ — ^^ — =r^  =  12.7  pounds  per  delivered  horse-power  hour. 
[j.oZ  X  245  X  77o 

When  called  upon  for  50%  overload  the  turbine  will  use 
more  steam  than  this  by,  say,  16%,  or  the  steam-channels 
must  be  so  designed  that  they  will  accommodate  14.8  pounds 
per  horse-power  hour,  when  the  machine  is  delivering  1500 
horse-power.    The  steam  used  will  then  be 

1500X14.8  =  22,200  pounds  per  hour, 
or  6.16  pounds  per  second. 

Let  the  pressure,  temperature,  and  heat  drop  in  the  three 
cyUnders  be  as  follows: 


Pressure  Absolute. 

Temperature  Drop. 

Heat  Drop. 

1.  160  to  45  pds.  sq.  in. . 

2.  45  to  10  ins.  mercury . . 

3.  10  ins.  to  29  ins 

824-735=   89° 
735-653=   82° 
653-540-113° 

86  B.T.U. 

80 

79       " 

Let  the  angles  of  exit  of  the  moving  blades  equal  tliose 
of  the  stationary  blades,  and  have  the  values  given  below, 
for  the  various  stages.  These  angles  are  varied  to  some  extent 
from  one  set  of  blades  to  another,  and  in  general  are  capable 


THE  IMPULSE-AND-RE ACTION  TURBINE.  221 


Fig.  78. 


222 


STEAM-TURBINES. 


of  being  "  gaged  "  or  set  as  may  be  found  necessary  for  obtain- 
ing  proper  axial  thrust  conditions. 


Cylinder 
No. 

steam 
Velocity. 

Peripheral 
Velocity. 

Angle  of 
Exit. 

1 
2 
3 

300 
430 
575 

140 

200 
250 

24° 

26i° 
30° 

The  velocity  diagrams  for  the  three  stages  may  now  be 

drawn,   as  in  Fig.   78,    and  the   work    done   in   each  row   of 

stationary  and    moving   blades    may  be    determined.      Thus, 

T    ^    .      V    1  ,  3002-1802     ^^^  ^ 

In  nrst  cylinder,  work  per  row  =  — ^r-r =  895  loot-pounds^ 

equivalent  to  1.15  B.T.U. 

Since  there  are  86  B.T.U.  given  up  in  this  cyhnder,  and 

since  the  work  in  the  moving  rows  is  the  same  as  that  in  the 

86 
stationary  rows,  there  will  be  ^  =  36  moving  and  36  stationary 

rows  of  blades  in  the  first  cylinder.  In  similar  manner  the 
number  of  blades  in  the  second  and  third  cyUnders  may  be 
found  with  the  following  result: 

Moving  blades — H.P.  end  of  spindle 36 

"           "         Middle  cylinder  on  spindle..  .  18 
"  "        L. P.  end  of  spindle 14 


Total 


68 


There  will  of  course  be  an  equal  number  of  rows  on  the  sta- 
tionary casing  of  the  machine. 

Diameter  of  Cylinders.— Assuming  the  speed  of  revolution 
of  the  turbine  as  2000  per  minute,  the  mean  diameters  of  the 
rows  of  blades  in  the  various  cylinders  is  fixed  by  the  assumed 
mean  peripheral  ve'ocity  of  blades. 

Cyl.  No.  Mean  Diameter. 

1 1.335  feet  or  16    inches. 

2 1.91      "    "  23 

3 3.97      "    "  47.5    " 


THE  IMPULSE-AND-RE ACTION  TURBINE.  223 

Length  of  Blades. — In  each  cyUnder  there  are  usually 
several  barrels,  each  containing  blades  of  a  given  length,  but 
the  blades  of  each  barrel,  advancing  from  the  high-pressure 
end  of  the  machine  towards  the  condenser,  are  longer  than 
those  of  the  prececUng  l)arrcl.  In  the  first  cylinder  there  may 
be  three  different  lengths  of  blade,  in  the  second  four,  and 
in  the  third  five  or  six.  The  variation  in  length  is  for  the 
purpose  of  increasing  the  cross-sectional  area  for  the  passage 
of  steam  as  the  latter  expands  in  volume.  The  proper  area 
for  any  section  of  the  turbine  may  be  calculated  by  finding 
the  volume  of  the  steam  at  that  section  from  the  curve  of 
volumes,  as  plotted  in  Fig.  77. 

The  mean  specific  volumes  of  the  mixture  of  steam  and 
water  while  passing  cyUnders  Nos.  1,  2,  and  3,  respectively, 
are,  approximately,  4,  16,  and  150  cu.  ft.  The  weight  of 
steam  passing  per  second  is  6.16  pounds,  and  the  exit  veloci- 
ties are  300,  430,  and  575  feet  per  second  for  the  three  cylin- 
ders respectively.     Therefore  the  mean  areas  should  be: 

6.16x4 
1st  cylinder,    '  =0.082  sq.  ft.  =     9.9  sq.  in. 

21        "         ^-^  =0.23    "    "  =  27.5  "    " 

3d        "         ^^|^"  =  1.60    ••    •'  =1920    "    " 

Making  the  same  assumption  as  to  blade  thickness  as  in  the 
previous  problem,  the  mean  blade  lengths  for  the  three  cylin- 
ders are 

1.5X9.9  ^^^„ 

^^=3l4^6"^"sh72r°    =0.73, -say  r; 

1.5X27.5 
^2  "  3.14  X  23  X  sin  26.5°~^-^^  ~'^^^  ^^  ' 

, 1-5x192  ^  „ 

^^"3.14x47.5Xsin  sqo-'^-^^ -^^y  '^s  • 


224 


STEAM-TURBINES. 


The  thickness  of  the  blades,  and  the  spacing  employed,  may 
be  such  that  the  blades  occupy  one-half  or  even  two-thirds  of 
the  annular  space  between  casing  and  spindle,  and  the  factor 
allowing  for  this  must  be  selected  accordingly. 


QUANTITIES  USED   IN   CHARACTERISTIC  CURVES   IN   FIG.  77. 


1 

2' 

3 

4 

5 

6 

7 

8 

T2 

{E,-Ei) 

■Eo 

Hy 

92 

x' 

x" 

X2  =  X'  +  X" 

540 

1.47 

1.96 

1058 

47 

0.750 

0.0995 

0.850 

575 

1.41 

1.80 

1034 

82 

0.783 

0.064 

0.847 

600 

1.36 

1.70 

1017 

107 

0.800 

0.049 

0.849 

650 

1.28 

1.51 

982 

158 

0.848 

0.030 

0.878 

700 

1.21 

1.35 

946 

208 

0.895 

0.016 

0.911 

750 

1.14 

1.21 

911 

259 

0.942 

0.007 

0.949 

800 

1.07 

1.09 

875 

311 

0.982 

0.002 

0.984 

824 

1.04 

1.04 

857 

335 

1.00 

9 

10 

11 

12 

13 

v  = 

=  X2(sp.  vol.at  r2) 

y 

//2  =  X'//^  +  (72 

II,- H^ 

i/  =  (//l-//2)(l-J/) 

558 

0.30 

841 

351 

245 

203 

0.22 

892 

300 

234 

107 

0.185 

921 

271 

221 

36 

0.145 

991 

201 

171 

15 

0.120 

1055 

137 

121 

7.0 

0.100 

1118 

74 

66 

3.7 

0.090 

1160 

32 

20 

0.075 

1192 

0 

0 

Hv  =  heat  of  vaporization  at  T2 ; 
92  =  heat  01  liquid  at  To', 
x'  =  quality  after  adiabatic  expan- 
E,~E.^ 


sion  to  T2,  =■ 


En 


Fig.  79. 


x"  =  increase  of  quality  due  to  fric- 
tion, =  ij{Hi-H^)^Hv; 

X2  =  quality  after  actual  expansion 

to  T.; 
v  =  volume  after  actual  expansion 

to  To; 
y  =  energy  loss ; 

Hi  =  ioia\.  heat  in  steam,  per  pd., 
at  Ti,  as  it  enters  turbine; 

.^2  =  total  heat  in  steam,  per  pd., 
after  adiabatic  expansion  to 
T2; 

H  =  heat  given  up  during  actual  ex- 
pansion to  T2. 


COMPARISON  OF  EFFICIENCIES.  225 

Comparison  of  Efficiencies  of  Single-stage  Impulse-  and 
Single-stage  Reaction-turbines. — The  expressions  for  the  hy- 
draulic efficiency  of  the  two  types  have  been  developed  in 
preceding  chapters  and  are  as  follows,  for  impulse-  and  for 
reaction-turbines  respectively :   • 

At/    r  W     1 

Impulse-turbine,    Efficiency  =  j^—  \  cos  a—y-[; 

11    {  u    \ 

Reaction-turbine,  Efficiency  =  y^  -!  2  cosa— •:r.-  \. 

These  equations  are   plotted  on  Plates   XIV  and  XV,  and 

11 
the  variation  of  maximum  efficiencv  with  -tt-  and  with  the 

angle  at  which  the  steam  leaves  the  nozzles  or  the  guide-blades 

is  shown  on  Plate  XVI. 

Expressed  numerically,  the  curves  on  Plate  XIV  show  the 

u 
following  values  of  the  ratio  tt-  for  the  conditions  stated: 

pr  for  Max.  Efficiency. 

■a  =  10° 49 

20° 48 

Impulse-turbme      j        o^o  44 

40° 38 

a  =  10° 97 

20° 93 

30° 87 

40° 80 


Reaction-turbine 


The  steam  velocities  used  in  the  impulse-turbine  are  much 
higher  than  in  the  reaction-turbine,  but  the  ratios  of  peripheral 
to  steam  velocity,  for  maximum  efficiency,  are  lower.  In  the 
compound  impulse-turbine  the  work  done  in  each  stage  is 
greater  than  that  done  in  the  reaction-turbine  per  stage,  and 
there  are  therefore  fewer  stages  in  the  impulse-turbine. 


226 


STEAM-TURBINES. 


In  the  impuise-turbine  the  efficiency  is  zero  when  cos  a  =  I 
and  u  =  V;  that  is,  when  the  jet  follows  directly  behind  the 
buckets,  with  the  same  velocity  as  the  buckets. 

Plate  XVII  shows  the  variation  of  efficiency  for  the  com- 
pound impulse-turbine,  with  a  and  u,  for  varying  number  of 
stages. 

In  the  reaction-turbine  the  efficiency  is  zero  when  cosa=l, 
and  u  =  2V. 

While  the  reaction-turbine  requires  a  greater  value  of  the 
11 
ratio  T^  for  maximum  efficiency  than  does  the  impulse-turbine, 

its  greater  number  of  stages  causes  the  steam  velocity  produced 
per  stage  to  be  much  lower.  This  permits  the  attainment  of 
satisfactory  efficiency  at  comparatively  low  peripheral  veloci- 
ties. The  following  particulars  applying  to  Parsons  turbines 
are  from  a  paper  by  Mr.  E.  M.  Speakman.* 
Electrical  Work. 


Peripheral  Vane  Speed. 

Number  of 
Rows. 

Normal  Output  of  Turbine. 

First  Expan- 
sion. 

Last  Expan- 
sion. 

tions  per 
Minute. 

5000  K.W 

135 
138 
125 
125 
125 
125 
120 
100 
100 

330 
280 
300 
360 
250 
260 
285 
210 
200 

70 

75 
84 
72 
80 
77 
60 
72 
48 

750 

3500  K.W 

1200 

2500  K.W 

1360 

1500  K.W 

1500 

1000  K.W 

750  K.W 

1800 
2000 

500  K.W 

3000 

250  K.W 

3000 

75  K.W 

4000 

Marine  Work. 


Type  of  Vessel. 

Peripheral 
H.P. 

^ane  Speed. 
L.P. 

Mean 
Ratio, 

M-i-F. 

Number 

of 
Shafts. 

High-speed  mail  steamers 

Intermediate  do 

70-  80 
80-  90 
90-105 
85-100 
10.5-120 
110-130 

110-130 
110-1.35 
120-1.50 
115-135 
130-160 
160-210 

0.45-0.5 

0.47-0.5 

0.37-0.47 

0.48-0.52 

0.47-0.5 

0.47-0.51 

4 
3  or  4 

Channel  steamers 

3 

Battle-ships  and  large  cruisers . 

Small  cruisers 

Torpedo  craft 

4 
3  or  4 
3  or  4 

*  Trans.  Inst,  of  Engineers  and  Shipbuilders  of  Scotland,  190.5-6. 


COMPARISON  OF  EFFICIENCIES. 


227 


Efficiency 


«  I 

Ol 

(5 

O 
P 
P- 

S 


^ 

^ 

^ 

^ 

^ 

^ 

^ 

s, 

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COMPARISON  OF  EFFICIENCIES. 


229 


Angle  of  entrance  to  moving  blades-degrees 


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230  STEAM-TURBINES. 

Heat  Analysis  of  Steam  Turbixes. 

In  as  much  as  the  calculations  by  means  of  which  the  steam 
passages  are  pro]3ortioned  presuppose  some  law  of  expansion  of 
the  steam  in  the  turbine,  it  is  very  desirable  that  such  tests 
of  completed  turbines  should  be  carried  out  as  would  show  to 
what  extent  the  performance  actually  attained  agrees  with  that 
assumed  as  the  basis  of  calculation  by  the  designer. 

An  analysis  of  a  turbine,  based  upon  heat  expenditure, 
should  show  what  percentage  of  the  available  heat  in  the  steam 
is  given  up  in  each  section  of  the  turbine.  Tliis  would  involve 
measurement  of  average  temperatures  and  pressures  where 
superheat  exists,  and  average  pressiu'es  and  qualities  where  the 
steam  is  not  superheated.  The  condition  of  the  steam  within 
a  turbine  in  operation  is  far  from  uniform  over  any  given  cross- 
section  of  the  steam  path,  and  it  is  therefore  necessary  to  take 
temperatures  and  qualities  at  many  different  depths  in  any 
steam  jDassage,  in  order  to  obtain  average  results  as  to  the  heat 
contents  of  the  steam. 

The  information  required  for  an  analysis  includes: 

(a)  Horse-power  delivered  from  the  turbine  shaft. 

(6)   Steam  used  per  unit  of  time. 

(c)  Average  pressures,  temperatures  and  qualities  at  certain 
points  along  the  turbine,  including  the  last  section. 

id)  The  weight  of  steam  collected  as  drainage-water,  if 
any,  from  the  various  parts  of  the  turbine. 

Assuming  that  determinations  of  quality  at  the  various  nozzle 
bowls  of  impulse  turbines,  and  between  the  sections  of  Parsons 
turbines  can  be  satisfactorily  made,  the  amount  of  heat  given 
up  by  the  steam  in  each  stage,  or  section,  may  be  determined. 
The  amount  of  water  drained  off  from  each  stage  should  be 
measured,  especially  in  the  case  of  impulse  turbines,  and  the 
hoat  so  carried  away  be  allowed  for.  A  curve  of  expansion  of 
the  steam  may  then  be  drawn  on  a  heat  diagram  (see  chart  on 
back  cover  of  book),  from  which  the  steam  consumption  may 
be  computed  for  a  turbine  supposetl  to  ha^•e  no  radiation  and 


HEAT  ANALYSIS. 


231 


bearing  friction  losses.  By  comparisons  of  this  steam  con- 
sumption witli  that  actually  determined,  per  B.H.P.,  by  test, 
the  factor  may  be  fouml  by  means  of  which  actual  steam 
consumption  may  be  predicted  from  the  curve  of  heat  given 
up,  as  drawn  on  the  heat-diagi'ani. 

Suppose  that  the  curve  on  the  temperature-entropy  chart 
shows  that  each  pound  of  steam  gives  up  185  B.T.U.  during  its 
passage  through  the  turbine.    Then  the  water-rate,  not  consid- 

( Initial  condition  of 
( superheated  steam 


( Condition  of 
"^    exhaust . 


Entropy 


Fig.  so. 

ering  the  external  losses  of  radiation   and  mechanical  friction 
would  be 

1,980,000 

778x:lS5  ^^^-^  pounds  per  H.P.-hour. 

Suppose  the  water-rate  is  found  from  the  test  to  be  16 
pounds  per  brake  horse-power-hom*.  This  means  a  useful  ex- 
penditure of 

1,980,000 
77Sy Ifi  ^^^^  B.T.I  .  per  pound  of  steam. 

Therefore  the  mechanical-friction  and  radiation  losses  use 
up  185—159=26  B.T.I',  for  each  pound  of  steam  passing 
through  the  turbine. 

Results  to  be  expected  from  a  given  design  may  be  predicted 


232  STEAM-TURBINES. 

by  means  of  expansion  curves  obtained  from  tests  of  similar 
turbines  as  follows: 

The  initial  pressure  and  superheat  or  quality  to  be  used 
having  been  determined,  and  the  vacuum  being  assumed,  the 
final  condition  of  the  steam  may  be  calculated,  corresponding 
to  a  given  water-rate. 

Thus,  if  the  water-rate  is  to  be  14  pounds  per  B.H.P.  hour, 
the  heat  usefully  employed  per  pound  of  steam  will  be 

1>980>000     109  RTF 

Besides  this  expenditure  of  heat,  the  surrounding  air  has  been 
heated  by  radiation  from  the  turbine,  and  also  the  surrounding 
air  and  the  oil  and  water  used  in  the  bearings  have  been  heated 
by  the  heat  appearing  as  bearing  friction.  Also,  the  water  drained 
from  the  turbine  has  carried  away  some  heat.  These  quantities 
of  heat  have  not  been  returned  to  the  steam  as  is  the  case  with 
the  heat  of  friction  between  the  steam  itself  and  the  passageways 
in  the  turbine.  The  quality  in  the  exhaust  pipe  will,  therefore, 
represent  a  smaller  final  heat  contents  than  that  obtained  by 
subtracting  182  B.T.U.  from  the  total  heat  in  the  entering  steam. 

Let  Hi  =heat  in  entering  steam  per  pound. 
7/pr  =  heat  appearing  as  B.H.P.  per  pound. 
Hl  =heat  appearing  as  the  losses  mentioned  above. 
H2  =  heat  in  exhaust  steam  per  pound. 
Then     H2=Hi-{Hw  +  Hl) 

Since  H2,  Hi  and  Hw  are  all  known  or  capable  of  deter- 
mination, the  amount  of  the  losses,  Hl,  may  be  found. 

Thus,  if  Hi  =1250  B.T.U.  per  pound, 

i^TF  =  182  B.T.U.  per  pound, 

H2  =1050  B.T.U.  as  found  by  calorimeter  deter- 
minations. 
Then,     Hl  =//i- i/^-i^ir^  1250 -1050 -182  =  18  B.T.U. 


HEAT  ANALYSIS.  233 

By  means  of  the  values  of  Hl  as  found  from  analyzing  turbine 
tests  in  the  above  manner,  the  conditions  of  expansion  in  a 
proposed  similar  design  may  be  predicted  and  the  i)roportions  of 
the  nozzles,  steam  passages,  etc.,  for  a  given  energy  distribution 
may  be  calculated. 

Example. — Suppose  a  turbine  receives  steam  at  17.")  pounds 
abs.  and  IGO  deg.  F.  superheat,  and  that  the  vacuum  is  28'' 
mercury. 

From  the  heat  diagram  the  initial  heat  contents  1298  B.T.U. 
Suppose  calorimeter  determinations  show  the  average  quality 
in  the  exhaust  from  the  last  set  of  buckets  or  blades  to  be  ,91. 
The  heat  contents  of  the  exhaust  as  found  from  the  heat  diagram 
■will  be  7^2' =  1020  B.T.U.,  approximately.  Let  the  water  rate 
be  found  by  test  to  be  11.5  pounds  per  brake  horse-power-hour. 

If  there  were  no  losses  due  to  mechanical  friction,  radiation, 
leakage,  etc.,  the  water  rate  would  be 

1,980,000  2545  2545     ^ 

77SX{H,-H,)  =  1298-1020  ^ ^78  =  ^-■^^  I^^^"'^^'  ^''' ^''''''' 

Due  to  the  losses,  Hl,  the  water  rate  is  raised  to  11.5  pounds,  or 

2545 
278~Hl^^^'^- 

Therefore,  the  external  losses  amount  to 

2545 
77,^  =  278-:,-^^.  =57  B.T.U. 

J-i.O 

If  the  steam  had  expanded  adiabatically  the  final  heat  contents 
Ho,  would  have  been  (from  the  heat  diagram)  930  B.T.U,  per 
pound,  and  the  steam  consumption 

2545 

=  0.91  pounds. 


1298-930 


6.91 
The  efficiencv  of  the  turbine  is  therefore  r^-^  =  ,60. 

11.0 


234  STEAM-TURBINES. 

A  steam  calorimeter  has  recently  been  brought  out  by  the 
author,  by  means  of  which  the  quality  may  be  determined  of  any 
steam  which  can  be  caused  to  pass  through  the  instrument. 
The  instrument  is  applicable  in  the  case  of  the  lowest  as  well  as 
the  highest  pressures  used  in  practice,  and  the  degree  of  wet- 
ness of  the  stean^  may  have  any  value  whatever  without  affect- 
ing^ the  accuracy  of  the  determinations.  The  problem,  how- 
ever, of  obtaining  representative  samples  of  steam  presents 
the  most  serious  obstacles  at  present  in  the  way  of  thermal 
analysis  of  steam  turbines. 

Amount  of  Superheat  to  be  Used  in  Turbines. — It  is  desirable 
that  the  degree  of  superheat  be  as  high,  but  not  higher,  than  that 
which  will  prevent  moisture  from  being  produced  before  the  steam 
has  passed  through  the  last  stage.  This  is  because  of  the  follow- 
ing: 

(a)  Moisture  in  the  steam  is  supposed  to  cause  losses  due  to- 
friction  between  steam  and  buckets,  and  to  increase  rotation 
losses. 

(6)  If  the  degree  of  superheat  is  great  enough  so  the  exhaust 


Fig.  81. 

is  superheated,  the  superheat  carried  away  by  the  exhaust  is 
lost. 

(r)  The  maintenance  of  superheaters  and  of  the  machinery 
in  general  is  more  expensive  the  higher  the  superheat. 

If  the  expansion  curve,  as  determined  from  the  temper- 
atures and  qualities  in  the  various  stages  of  actually  testea 
turbines  ends  at  A,  Fig.  81,  it  is  evident  that  the  degree  of 


HEAT  ANALYSIS.  235 

superheat  is  too  low  and  that  some  of  the  stages  are  working 
hi  wet  steam  with  the  consecjuent  losses. 

If  the  expansion  curve  ends  at  B,  there  is  superheat  in  the 
■exhaust,  and  resulting  loss  of  efhciency  caused  by  too  high 
initial  superheat. 

A  curve  C,  representing  the  correct  condition  of  the  exhaust, 
may  be  drawn  on  the  diagram,  similar  in  character  to  the  curve 
of  expansion  already  determined,  and  indicating  approximately 
the  degree  of  superheat  which  will  be  necessary  in  order  that 
the  exhaust  may  be  just  dry  and  saturated. 

Description  of  the  Calorimeter. — Figures  82  and  83  show 
the  exterior  and  the  general  interior  arrangement  of  a  steam 
calorimeter  with  which  the  quality  of  any  st(^am  passing  through 
the  calorimeter  can  be  determined  with  accuracy  in  a  ver}^  simple 
manner.  The  instrument  is  especially  designed  for  determining 
the  quality  of  steam  at  different  points  along  steam  turbines, 
and  it  can  be  used  with  steam  of  any  degree  of  wetness  and  of 
any  temperature  and  pressure  above  that  in  the  condenser. 
The  sampling-tube  leading  to  the  calorimeter,  and  shown  in  Fig. 
86,  may  be  extended  into  any  steam  passage  from  one  part  of 
the  turbine  to  another,  and  the  average  quality  may  thus  be 
investigated  by  taking  successive  samples  from  different  depths. 
From  this  information,  combined  with  the  results  of  ordinary 
tests,  a  curve  may  be  drawn  on  a  heat  diagram,  showing  the 
distribution  of  the  work  done  by  the  steam  in  the  turbine,  and 
indicating  the  efficiency  of  the  various  sets  of  blades  or  buckets. 
Such  a  curve  may  also  be  used  to  indicate  the  degree  of  initial 
superheat  that  should  be  used  in  the  entering  steam  in  order 
that  the  steam  at  any  set  of  blades  may  be  in  a  given  desired 
condition  as  to  heat  contents. 

The  difficulty  of  obtaining  a  representative  sample  of  steam, 
especially  under  the  complex  conditions  existing  in  steam  tur- 
bines, is  fully  recognized,  and  the  sampling-tube  shown  in  Figs. 
■85  and  86  has  been  designed  to  assist  in  obtaining  definite  results. 
With  this  tube  it  is  at  least  possible  to  obtain  samples  from  given 
definitely  known  depths  or  positions  in  a  steam  passage. 


236 


STEAM-TURBINES. 


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HEAT  ANALYSIS.  237 

The  development  of  the  instrument  resulted  from  experiments 
in  passing  steam  from  an  electrically  heated  calorimeter  through 
a  transparent  glass  tube.  If  the  electrical  energy  supplied  to 
the  steam  in  passing  through  the  calorimeter  was  insufficient  to 
dry  the  steam,  water  could  be  seen  in  the  interior  of  the  glass 
tube;  also  no  rise  of  temperature  was  shown  on  a  thermometer 
placed  in  the  tube.  By  adding  sufficient  electrical  energy  to 
the  steam,  the  interior  of  the  tube  cleared  up  because  of  the 
disappearance  of  the  water,  and  the  temperature  began  to  rise 
at  the  same  instant  that  the  steam  gave  this  evidence  of  being 
completely  dry.  It  was  therefore  possible  to  measure  directly 
the  amount  of  heat  required  to  dry  the  sample  of  steam,  and 
from  the  known  heat  of  vaporization  of  dry  steam,  and  the 
known  weight  of  steam  passing  through  the  calorimeter,  the 
quality  could  be  readily  found.  The  method  of  ascertaining  the 
weight  of  steam  passing  per  unit  of  time  is  described  in  the 
following  paragraph. 

In  operation  the  calorimeter  is  attached  to  the  sampling-tube, 
or  to  the  source  of  steam  directly,  by  means  of  the  screw-thread 
A.  Steam  is  thus  admitted  to  the  instrument,  from  which  it 
passes  to  the  condenser  or  to  the  atmosphere,  through  a  pipe 
from  the  discharge  valve,  placed  at  C.  Having  adjusted  the 
discharge  valve  so  it  is  passing  a  suitable  quantity  of  steam, 
enough  energy  is  turned  in  to  heat  the  steam  to  dryness.  The 
condition  of  diyness  is  indicated  by  an  immediate  rise  of  tem- 
perature as  shown  by  the  thermometer,  if  more  than  the 
requisite  amount  of  electrical  energy  is  supplied.  For  con- 
venience let  the  watts  necessary  to  dry  the  steam  be  called  Ei. 
After  noting  this  number  of  watts  the  steam  is  further  heated  by 
additional  watts  E2,  till  a  temperature  T  degrees  above  sat- 
uration is  obtained,  say  20,  30,  100,  or  some  other  convenient 
number  of  degrees  superheat.  This  operation  is  for  the  purpose 
of  ascertaining  the  weight  of  dry  steam  per  hour,  TT^i,  which  was 
passing  when  the  steam  was  just  diy.  The  weight  W2,  passed 
through  the  valve  after  superheating,  will  be  less  than  the  dry 
steam  passed  through,  by  some  percentage  represented  by   a 


238  STEAM-TURBINES. 

constant,  C,  because  of  the  increase  in  volume  accompanying 
superheating.  This  has  been  determined  by  test  witli  the  in- 
struments. Also,  the  watts  S,  necessary  to  superheat  a  pound  of 
steam  to  T  degrees,  at  different  pressures,  have  been  determined. 
The  latter,  S,  may  be  used  instead  of  the  specific  heat  of  steam 
and  has  the  advantage  of  allowing  automatically  for  radiation 
losses.  The  quality  of  the  steam  may  be  obtained  either  by  use 
of  the  curves  supplied  with  the  calorimeter,  or  by  the  use  of  the 
specific  heat  of  steam  for  varying  pressures.  The  use  of  the 
curves,  however,  eliminates  entirely  possible  errors  due  to  un- 
certainty as  to  the  value  of  the  specific  heat. 

Let  Tl^i  =  weight  of  dry  steam  passing  per  hour. 

Then    Ei    watts    evaporates    the  moisture  in  Wi   pounds 

,     ,  .  .  .     ,  3.412^1    , 

per  hour   and   this   energy  is   equivalent   to  — rp —    thermal 

units  per  pound  of  steam.  Let  this  amount  of  heat  be  repre- 
sented by  H^.  Let  W-z  =  weight  of  superheated  steam  passing  per 
hour  =  CTFi.  Then  E2  watts  raises  the  temperature  of  CWx 
pounds  of  steam  through  T  degrees,  or  E2  =  CWiS  watts, 
where  S  represents  the  watts  required  to  superheat  one  pound  of 
steam  per  hour  through  T  degrees,  at  the  pressure  in  the  calori- 
meter. 

Then,  "^'1  =  ^' 

and  this  value  of  W\  may  be  substituted  in  the  equation, 

3.412^1 


H.^ 


Thus,  H  = 


1^1     • 

3.412^iXC*Sf 
E2 


Since  C  and  S  are  constants  for  any  given  pressure  and  degree 
of  superheat,  3.412  CS  may  be  written  as  a  constant,  K,  and 
values  of  this  constant  are  given  for  varying  pressures  and  de- 


HEAT  ANALYSIS.  239 

grees  of  superheat,  by  a  set  of  curves  plotted  from  experiment- 
ally obtained  data.    See  Fig.  82. 
The  equation  then  becomes 

J2J2 

If  H  represents  the  heat  of  vaporization  of  dry  steam  (from 
steam  tables)  at  the  pressure  indicated  by  the  original  temperature 
in  the  calorimeter,  the  quality  of  the  steam  passing  through  the 
calorimeter  is 


x= 


H. 


It  is  to  be  noted  that  the  constant  K  is  independent  of  the 
weight  of  steam  flowing  through  the  calorimeter  during  super- 
heating, although  consideration  of  this  weight  has  been  included 
in  the  explanation  just  given.  The  same  result  may  be  found 
without  the  use  of  either  C  or  S.  The  independence  of  K  upon, 
these  quantities  may  be  shown  as  follows: 

As  defined  above, 

C  =  ^^,    and     S  =  ^^. 

K  =  3A12SC  =  SA12X^X^J-^. 
W2     Wi        Wi 

It  is  therefore  possible  to  find  the  expression  for  K  without 
using  C  or  S.  Thus,  if  the  steam  flowing  through  the  calori- 
meter is  first  dried,  by  the  introduction  of  Ei  watts,  then  super- 
heated through  T  degrees  by  a  further  introduction  of  E^  watts, 
it  follows  that  for  each  pound  of  the  original  weight  IFi  of  dry 

E  2 
steam,  it  has  taken  T77-  watts  to  superheat  the  steam  coming 

from  Wi  pounds  of  diy  steam,  tlii'ough  the  given  temperatm-e 

range  T.     Hence,  for  the  pressure  and  temperature  in  question, 

E2  .  .  E2 

T^T~  IS  a  constant,  which  may  be  called  k,  and  Wi^~. 


240  STEAM-TURBINES. 

Substituting  this  value  of  TFi  in  the  equation  Hx=  — W- — , 
„      3.412^i/>; 


E, 


Let  3.412^•  be  called  K. 


El 
Then  Hx=Kw^,  as  before  found. 

£,2 

Summing  up  the  operations  involved  in  determining  the 
quality  of  steam,  they  are  as  follows: 

1.  The  calorimeter  is  attached  to  the  source  of  steam  and  a 
flow  of  steam  takes  place  through  the  electrical  heating  coils, 
and  out  through  the  discharge  valve  at  C,  Fig  83.  Electrical 
connections  are  made  with  an  ordinary  D.  C.  circuit  at  perhaps 
125  volts,  capable  of  carrying  10  amperes.  The  calorimeter  is 
put  in  series  with  the  water  rheostat,  and  means  are  provided 
for  measuring  the  input  of  electrical  energy. 

2.  Electrical  energy  is  supplied  sufficient  not  only  to  dry  the 
steam,  but  to  superheat  it  to  some  convenient  temperature. 
The  watts  introduced  are  called  Et-  Now  turn  out  energy  until 
superheating  no  longer  takes  place,  and  the  steam  is  therefore 
just  dry.  The  energy  now  being  introduced  is  only  that  neces- 
sary to  dry  the  steam,  and  is  called  E^.  The  condition  of  dry- 
ness is  indicated  as  before  described.  Then  Et  —  Ei  =  E2  watts 
required  to  superheat  through  T  deg. 

3.  From  the  curves  select  the  value  of  the  coefficient /v  corres- 
ponding to  the  degree  to  which  the  steam  was  superheated,  and 
to  the  original  temperature  in  the  calorimeter,  and  find  the  heat, 

*  The  constant  3.412  is  the  number  of  B.T.U.  equivalent  to  1  watt-hour. 

Its  development  may  be  shown  as  follows: 

1  horse-power  hour  is  equivalent  to  33000x60  or  1,980,000  foot-pounds. 

1  B.T.U.  is  equivalent  to  778  foot-pounds. 

1,PS0,C00 
Therefore,  1  horse-power  hour  is  equivalent  to '- 2545  B.T.U, 

778 

But  1  horse-power  hour  is  also  equivalent  to  746  watts. 

2545 
Therefore,  1  watt-hour  is  equivalent  to  -——-=3  412  B.T.U. 


HEAT  ANALYSIS.  241 

Hx,  which  has  boon  added  to  each  pound  of  steam  in  order  to  (hy 

El 
it,  from  the  ccjuation  Hr  =  K-fr. 

4.  Find  the  quality  of  steam  from  the  second  set  of  curves, 

rj  TT 

Fig.   83,  representing  the  equation  x=—^ — -.     The  quahty 

may  of  course  bo  found  directly  from  the  equation  if  desired. 

The  question  may  be  asked,  why  not  call  the  watts  required 
to  diy  and  superheat  the  steam  Ei  +  E2,  instead  of  Et.  It  will 
be  seen  upon  reflection  that  when  diying  and  superheating  are 
taking  place  together,  Ei,  as  prevoiusly  defined,  is  not  being 
introduced  to  dry  the  steam,  because  the  steam  passing  tlu'ough 
the  orifice  or  valve  at  outlet  from  the  calorimeter  is  less  during 
superheating  than  during  drying  of  the  steam,  and  therefore 
the  heat  necessaiy  to  diy  the  steam  passing  through  the  calori- 
meter is  less  then  Ei.  As  soon  as  E2  has  been  turned  out,  and 
the  steam  is  just  diy,  Ei  is  again  being  introduced,  but  Ei  and 
E2,  as  defined,  are  not  simultaneously  introduced. 

Example  No.  1. — Let  wet  steam  be  passing  through  the  cal- 
orimeter at  a  temperature  of  3(36  deg.  F.,  as  shown  by  the  ther- 
mometer in  the  tube  B.  This  corresponds  to  a  pressure  of  165 
pounds  per  square  in.  abs.  Let  650  watts  {  =  Et)  be  introduced, 
and  let  the  resulting  temperature  be  460  deg.  The  steam  has 
then  been  not  onl}'  dried,  but  superheated  through  a  range  of 
94  deg.  {=T).  Let  the  energy  be  now  reduced  until  the  steam 
is  just  diy,  and  let  the  watts  then   being   introduced  be  260 

E2-Et-Ei  =  650  -  260  =  390. 

From  the  curves  the  value  of  K  corresponding  to  this  pressure 
and  to  r  =  94  deg.,  is  A' -59.0. 

260 
Therefore,  Hx  =  ^^^  X  59.0  =  39.4, 

and  from  the  curves  of  (juality,  x  =  9oA  per  cent. 

Example  No.  2. — Let  the  pressure  as  indicated  by  the  tem- 
perature of  153  deg.  in  the  calorimeter  be  4  pounds  abs. 


242 


STEAM-TURBINES. 


Let  £"7  =  480  watts,  and  let  the  resulting  temperature  =  240 
deg.,  corresponding  to  a  range  of  87  deg.  superheat. 

Let  Ex  be  found  to  equal  360  watts.  Then  £^2= 480 -360  = 
120. 

From  the  curves,  A' =  43.."), 

//,  =  ^X43.5  =  116. 

From  the  curves  of  ([uality, 

x  =  88.7  per  cent. 

The  calorimeter  is  supplied  with  a  w^ater  rheostat  box  which, 
serves  to  control  the  amount  of  electrical  energy  introduced, 
and  also  for  carrying  the  calorimeter  and  accessories.  The 
complete  outfit  is  shown  in  Fig.  84  together  with  a  separate  cover 


A  B 

A — Calorimeter  Outfit  Complete. 

B — Cover  of  Water-rheostat  Box,  Fitted  with  Adjustable  Terminal. 

Fig.  84. 

for  showing  how  the  rheostat  is  operated.  WTien  the  box  is 
in  use  as  a  water  rheostat  the  cover  holds  a  nut  in  which  a  screw, 
D,  works  for  raising  or  lowering  the  cone  E,  and  thus  varying  th'i 
energy  passing  the  rheostat.     The  lower  terminal  connection  is 


HEAT   AXALYSIS. 


243 


o 

fa 


244  5  TEA  M-  T  URBINES. 

shown  at  F,  on  the  box,  and  the  upper  is  at  G,  in  the  swivel  nut 
on  top  of  the  operating  screw.  The  box  is  about  13  inches  high, 
and  the  outfit  complete  weighs  about  43  pounds.  When  the 
calorimeter  is  in  the  box  it  is  attached  to  the  iron  plate  forming 
the  lower  terminal  of  the  rheostat  on  the  bottom  of  the  box,  by 
means  of  the  screw  thread  A,  and  the  top  of  the  calorimeter 
projects  through  the  top  of  the  box  one-half  inch.  The  brass 
handle  is  tapped  out  and  screws  on  the  top  of  the  calorimeter 
for  convenience  in  carr3dng  the  outfit. 

The  cover  shown  at  the  right  of  Fig.  84  belongs  to  another 
rheostat,  not  to  the  complete  outfit  shown  at  the  left  of  the  fig- 
ure. The  box  to  the  left  sho^^•s  the  calorimeter  outfit  ready  for 
transportation.  The  terminal  shown  on  the  outside  of  the  box 
can  be  unscrewed  and  carried  with  the  other  accessories  inside 
the  box. 

The  glass  outlet  from  the  calorimeter  is  not  a  necessar}^  part 
of  the  instrument,  since  the  condition  of  diyness  is  indicated 
by  the  rise  of  the  mercury  in  the  thermometer,  but  it  is  useful 
as  giving  an  optical  demonstration  that  the  steam  has  heen  com- 
pletely dried,  and  also  in  affording  an  excellent  means  for  study- 
ing the  behavior  of  wet  and  of  superheated  steam. 

The  sampling-tube  shown  in  Figs.  85  and  86  permits  of 
taking  consecutive  samples  of  steam  from  different  depths  in 
any  steam  passage.  There  are  two  tubes,  of  which  the  outer  is 
stationary,  and  the  inner  can  be  rotated  by  means  of  the  hand- 
wheel  and  bevel-gear  connections.  The  outer  tube  is  slotted 
over  its  entire  length,  while  the  inner  tube  contains  short  slots 
which  open  consecutivel}'  into  the  long  slot  in  the  outer  tube. 
It  is  thus  possible  to  take  samples  from  the  different  portions  of 
a  steam  passage  without  disconnecting  the  calorimeter,  and  to 
know  positively  from  what  part  the  sample  is  being  drawn. 


CIL\PTER  IX. 

TYPES   OF  TURBIXE  AND  THEIR   OPERATIOX. 

Detailed  descriptions  of  the  steam-turbines  in  use  at  the 
present  time  are  available  in  catalogues,  and  in  technical  books 
and  papers,  so  that  in  the  following  discussion  only  the  dis- 


FiG.  87. — Simple  impulse-wheel,  De  Laval  type. 

tinctive  features  of  certain  representative  types  will  be  dealt 
with. 

The  turbines  that  have  been  developed  commercially  in 
this  country  are  of  three  types:  (a)  the  De  Laval;  (6)  the 
Parsons;    (c)  the  Curtis. 

The  De  Laval  Turbine  is  shown  in  Figs.  87  to  9L  It  is  a 
simple  impulse-turbine,  consisting  essentially  of  a  single  wheel 
or  disk,  upon  the  rim  of  which  are  mounted  buckets,  or  blades, 
which  receive  impulse  from  a  set  of  expanding  nozzles  delivering 
steam  at  high  velocity.    The  buckets  are  placed  radially  around 

24.5 


246 


STEAM-TURBINES. 


WOODRUFF  KEY       B 


TYPES  OF   TURBINE  AXD   THEIR  OPERATION. 


2i-i 


the  circumference  of  the  wheel,  and  the  nozzles  are  distributed 
about  the  circumference  as  shown  in  Fig.  87. 


Fig.  89  — De  Laval  turbine  rotor. 

The  essential  parts  of  this  turbine  are: 

(a)  The  nozzles,  in  which  the  steam  expands  to  the  con- 
denser pressure,  and  attains  the  maximum  possible  velocity 
under  the  conditions  of  operation. 

(b)  The  blades,  or  buckets,  which  change  the  direction  of 


Fig.  00  — De  Laval  nozzle  and  valve. 

the  flow  of  steam,  and  thereby  transform  the  energy  of  the 
jet  into  useful  work  in  turning  the  shaft  upon  which  the  wheel 
is  mounted. 

A  distinguishing  feature  of  this  type  of  turbine  is  the  high 
speed  of  rotation  of  the  wheel.  This  is  made  necessary  because, 
in  order  efficiently  to  utiHze  the  energy  of  the  steam-jet,  the 
peripheral  velocity  of  the  buckets  must  be  from  0.35  to  0.5  of 
the  velocity  of  the  steam  lea^'ing  the  nozzles.  The  high  periph- 
eral velocity  could  be  obtained  at   a  low  speed  of  revolution 


248 


STEAM-TURBINES. 


if  the  wheel  diameter  were  to  be  made  correspondingly  large. 
But  large  diameters  are  impracticable  because  of  the  frictional 
forces  which  would  be  brought  into  play,  and  certain  pro- 
portions have  been  found  which  permit  of  a  reasonable  peripheral 
speed  and  allowable  stresses  in  material  of  the  wheel  or  disk. 
The  speed  of  revolution,  however,  remains  high,  and  can  be 
utihzed  for  driving  machinery  only  by  the  use  of  gearing. 
The  number  of  revolutions  per  minute  varies  from  SOOO  or 


De  Laval  governing  mechanism. 


10,000,  in  300-horse-power  turbines,  to  25,000  or  30,000,  in 
very  small  machines.  Since  it  is  impracticable  perfectly  to 
balance  a  wheel  of  the  type  used,  a  light,  flexible  shaft  is 
employed,  which  allows  the  wheel  to  assume  its  proper  center 
of  rotation,  and  thus  to  operate  Uke  a  truly  balanced  rotating 
body. 

The  De  Laval  turbine  has  the  advantage  of  developing 
a  large  amount  of  power  per  unit  of  weight,  and  is  readily 
apphed  to  the  driving  of  electric  generators,  centrifugal  pumps, 
and  blowers. 


TYPES  OF   TURBINE  AND    THEIR  OPERATION. 


249 


DE  LAVAL  300-HORSE-POWETl  TURBINE-TESTS,  CONDUCTED  BY 
MESSRS.  DEAN  AND  MAIX. 

Te.'^t.s  with  S.\tur.\ted  Ste-vm. 

Number  of  nozzles  open,  eight  (8"). 
Average  reading  of  barometer,  29.92  in. 
Average  temperature  of  room,  90°  F. 


Date, 
1902. 

Hour. 

Feed -water 
Weighed  per 
Hour,  Lbs. 

-  t,  c 

Moi.stureinSteam 
at  Throttle  by 
Calorimeter. 

Dry  Steam  En- 
tering Turbine, 
Lbs. 

lis 
m 

Oh 

Pressure  below 
Governor- 
valve,  Lbs. 

S 

3 
3 

si 
> 

_5 

■Be 

^  c 

o 

Dry  Steam  used 
per  Brake  H. P. 
per  Hour,  Lbs. 

May  23 
May  23 
May  23 
May  23 
May  23 
May  23 
May  23 
May  23 

8.15  a.m. 

9.15  a.m. 

9.15  a.m. 
10.15  a.m. 
10.15  a.m. 

11  .  15  .\.M. 
1  1  .  15  K.M. 
12.15A..M. 

1  5289 
1  5073 
1  5286 
1  5283 

70 
70 
70 
70 

2.15% 
2.15% 
2.15% 
2.15% 

5107 
4896 
5104 
5101 

204.7 
206.2 
207.2 
207.4 

196.2 
196.2 
196.3 
198.9 

26.7 
26.6 
26.6 
26.6 

332.2 
332.4 
332.2 
334.9 

15.37 
14.73 
15.37 
'15.23 

Inde- 
pentlent 
Average 

8.15  a.m. 
12.15  P.M. 

\  5233 

70 

2.15% 

5052 

206.4 

196.9  26.6 

747 

333.0 

15.17 

Number  of  nozzles  open,  seven  (7). 
Average  reading  of  barometer,  29.90  in. 
Average  temperature  of  room,  97°  F. 


Mav  23 
Mav  23 
Mav  23 
May  23 


Inde- 
pendent 
Average 


12.45  p.m. 
1 .45  p.m. 
1 .  45  P.M. 
2.45  P.M. 


12.45  p.M, 
2.45  p.M 


4675|    60     2.15%'   4516 
4499     60    l2.15%     4344 


}  4587     60     2.15%:  4430 


207.0 
207.7 


207.3 


196.6 
196.4 


196.5 


26.8     .. 
26.8     .. 


26.8      746 


284.4 
285.2 


284.8 


15.88 
15.23 


15.56 


Number  of  nozzle.''  open,  five  (5). 
-Vverage  reading  of  barometer,  29.83  in. 
Average  temperature  of  room,  97°  F. 


Mav  23 
May  23 
Mav  23 
May  23 

3.00  P.M. 
4.00  P.M. 
4.00  P.M. 
5.00  P.M. 

1  3483 
\  3219 

51 
51 

51 

2.15% 
2.15% 

3358 
3100 

207.5 
207.8 

196.5 
195.1 

27.3 

27.4 

194.8 
195.6 

17.24 
15.85 

Inde- 
pendent 
Average 

3.00  P.M. 
5.00  P..M. 

\  3351 

2.15% 

3229 

207.6    195.8 

27.35 

751 

195.2 

16.54 

Number  of  nozzles  ojien,  three  (.3). 
Average  reading  of  barometer,  29.81  in. 
Average  temperature  of  room,  80°  F. 


June  10 
June  10 
June  10 
June  10 
June  10 
June  10 

6.35  P.M. 
7.35  P.M. 
7.35  ,.M. 
8.35  P.M. 
8.35  p.m. 
9.35  P.M. 

1   199G 
1  209S 
1   1984 

33 
33 
33 

2.15% 
2.15% 
M5% 

1921 
2021 
1909 

201.1 
201.6 
201.7 

196.5 
198.9 
198.4 

28.1 
28.1 
28.1 

115.0 
122.0 
121  5 

16.70 
16.57 
15.71 

Inde- 
pendent 
Average 

6  35  P.M. 
9.35  P.M. 

}  2026 

33 

2.15% 

1950 

201.5 

197.9 

28.1 

751 

118.9 

16.40 

All  barometer  readings  are  reduced  to  32°  F. 


250 


STEAM-TURBINES. 


Tests  with  Superheated  Steam. 


Number  of  nozzles  open,  eight  (8). 
Average  reading  of  barometer,  30.18  in. 
Average  temperature  of  room,  8.3°  F. 


Date, 
1902. 

Hour. 

Weight 

of 
Steam 
U.9ed 
per 
Hour, 
Lbs. 

Pres- 
sure 
abo^'e 
Gov- 
ernor- 
valve, 
Lbs. 

Pres- 
sure 
below 
Gov- 
ernor- 
valve, 
Lbs. 

Vacu- 
um, 
Ins. 

Super- 
heat 
Gov- 
ernor- 
valve. 

Revs, 
per 
Min- 
ute of 
Gene- 
rators. 

Brake 
Hor.se- 
power. 

Steam 
Used 

per 
Brake 
Horse- 
power 

per 
Hour, 

Lbs. 

May  22 
May  22 
May  22 
May  22 
Mav  22 
May  22 

8-    9  A.M. 

9-10  A.M. 
10-11  A.M. 
11-12  A.M. 
12-    1    P.M. 

1-    2  P.M. 

4833 
4936 
5083 
4976 
4841 
4768 

208 . 3 
207.5 
207.7 
208.3 
207.5 
206.9 

200.6 
199.3 
202,1 
199.4 
194.3 
195.6 

27  2 
27.2 
27.2 
27.2 
27.3 
27.2 

81°  F. 
86°  F. 
91°  F. 
88°  F. 
82°  F. 
75°  F. 

356.6 
355.7 
357.8 
354.1 
343.5 
344.4 

13. 55 
13.88 
14.21 
14.05 
14.09 
13.84 

Inde- 
pendent 
Average 

8-  2  P.M. 

4906 

207.0 

198.5 

27.2 

84°  F. 

750 

352.0 

13.94 

Number  of  nozzles  open,  seven  (7). 
Average  reading  of  barometer,  30.07  in. 
Average  temperature  of  room,  90°  F. 


Mav  22 
May  22 

May  22 
May  22 

2.10  P.M. 
3.10  P.M. 
3.10  P.M. 
4.10  P.M. 

\  4316 
1  4248 

207.5 
207.3 

196.2 
197.9 

27.4 
27.4 

67°  F. 
61°  F. 

299.8 
297.3 

14.39 
14.29 

Inde- 
pendent 
Average 

2.10  P.M. 
4.10  P.M. 

1  4282 

207.4 

197.0 

27.4 

64°  F. 

756 

298.4 

14.35 

Number  of  nozzles  open,  five  (5). 
Average  reading  of  barometer,  29.79  in. 
Average  temperature  of  room,  89°  F. 


June  10 
June  10 
June  10 
June  10 
June  10 
June  10 

8.45  a.m. 

9.45  A.M. 

9.45  A.M. 
10.45  a.m. 
10.45  a.m. 
11.45  a.m. 

1  3068 
\  3010 
}  3020 

199.2 
201.5 
201.4 

196.5 
197.2 
196.1 

27.6 
27.4 
27.4 

8°  F. 
12°  F. 
10°  F. 

195.3 
197.3 
196.5 

15.71 
15.26 
15.37 

Inde- 
pendent 
Average 

8.45  a.m. 
11.45  a.m. 

}  3033 

200.7 

196.6 

27.5 

10°  F. 

743 

196.5 

15.44 

June  10 
June  10 
June  1 1 
June  10 
June  10 
June  10 

1.45  P.M. 
2.45  p.m. 
2.45  P.M. 
3.45  P.M. 
3.45  P.M. 
4.45  P.M. 

1  3107 
j   3054 
1  3025 

201.4 
203.1 
202.7 

196.7 
199.0 
197.5 

27.4 
27.3 
27.4 

13°  F. 
15°  F. 
19°  F. 

194.8 
197.9 
194.7 

15.95 
15.43 
15.54 

Inde- 
pendent 
Average 

1.45  P.M. 
4.45  P.M. 

}  3062 

202.4 

197.7 

27.4 

16°  F. 

747 

196.0 

15.62 

Average  of  both  tests 745 


15.53 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


251 


The  following  table  *  gives  results  of  acceptance  tests  made 
upon  a  300-liorse-power  De  Laval  turbine  in  November,  1904: 

Machine  No.  2083.  Nov.  18,  1904. 

Result  Sheet. 


Run  No 

Duiation  of  run,  minutes 

Re^■olut.ions    of    generator-shafts 

per  minute 

Steam-pressure   abo\-e    go\ernor- 

vulve,  pounds,  gage 

Steam-pressure    below    go\-ernor- 

Aalve 

Load  in  per  cent  of  rated  load. .  .  . 

Vacumn,  inches  mercury 

Back  pressure,  pds.  sq.  in.  al:>s..  . 

Number  of  nozzles  open 

Quality  of  steam,  per  cent 

Superheat  of  .steam,  deg.  F 

Total  D.  H..  P 

' '      steam  per  hour,  pounds .  .  .  . 
Steam  per  D.  H.  P.  hour,  pounds 

Total  K.W 

Steazn  per  K.W.  hour,  pounds  .  .  . 


1 
55 

907 

152 

133 

1 

27*25 

1.60 

4 

100 


9S.1 
2286.4 
23.3 
56 .  63 
40.4 


2 
55 

897 

152 

144 

i 

27.19 

1.64 

5 
100 


159.5 
3049.0 
19.1 
100.38 
30.35 


3 

55 

900 

152 

140 

26*85 
1.84 

7 
100 


236 

4183.9 

17.71 

155.2 

26.95 


4 
55 

898 

152 

136 

1 

26.20 

2.14 

9 
100 


302 . 5 
5326.5 
17.6 
201.13 
26.5 


5 
55 

895 

152 

140 

H 

25.75 

2.36 

10 

19.9 

348 

6145.0 

17.64 

233.2 

26.35 


The  Parsons  Turbine  embodies  a  combination  of  the  impulse 
and  reaction  principles.  The  steam  expands  during  its  passage 
through  the  Parsons  turl^ine  much  as  it  does  in  an  expanding 
nozzle;  that  is,  the  cross-sectional  area  of  steam-passage  increases 
from  the  high-  to  the  low-pressure  end  of  the  turbine,  according 
to  the  volume  and  velocity  of  the  steam  at  the  various  points 
of  its  path.  The  annular  space  between  the  stationary  casing 
and  the  rotating  spindle  corresponds  essentially  to  a  simple 
steam-nozzle,  ^^ith  the  difference  that  in  a  nozzle  the  heat 
energy  is  expended  upon  the  steam  itself  in  producing  high 
velocities  of  efflux;  whereas,  in  the  turbine,  the  kinetic  energy 
of  the  steam  due  to  the  heat  drop  in  any  one  stage  is  expended 
in  producing  rotation  of  the  spindle. 

The  heat  given  up  in  any  one  stage  is  limited  to  that  amount 
which  will  produce  the  kinetic  energy  desired  to  be  absorbed 
in  that  stage.  Further  increments  of  heat  drop  in  succeecUng 
stages  add  successive  increments  of  rotative  effort  to  the  spindle, 


*  Tliesis  test  of  Messrs.  Crosier  and  Little,  Sibley  College,  1905. 


252 


STEAM-TURBINES. 


until,  when  the  steam  has  passed  entirely  through  the  tur- 
bine, it  has  fallen  in  temperature  and  pressiu-e  an  amount 
corresponding  to  the  total  heat  given  up  as  work,  plus  the 
losses  experienced  in  the  machine. 

The  fact  that  the  heat  drop  is  divided  into  a  great  num- 
ber of  steps,  the  energy  being  absorbed  as  rotative  effect  during 
each  step,  causes  the  steam  velocity  to  be  kept  low  throughout 
the  macliine,  and  allows  a  comparatively  low  peripheral  speed 
of  blades  to  be  employed  with  good  efficiency. 

The  general  arrangement  and  various  details  of  the  Par- 
sons turbine,  as  manufactured  by  the  Westinghouse  Macliine 
Company,  are  shown  in  Figs.  93-100. 

The  curves  in  Fig.  92  show  economy  attained  by  the  use 
of  saturated  steam  and  superheated  steam,  and  the  effect 
of  increase  of  vacuum. 

The  table  below  gives  the  trial  results  represented  by  the 


Gage  Pressure. 

Steam  Consumption 

Degrees 
Super- 
heat, F. 

Vacuum, 
Inches  of 
Mercury. 

Brake 
Horse- 
power. 

Before 
Entering 
Throttle. 

After 
passing 
Throttle. 

Per 
Hour, 
Total. 

Gland 
Leakage. 

Net  per 
Hour. 

Per 
B.H.P. 
Hour. 

152 

About 

97    . 

27.3 

269 

4352 

339 

4013 

14.9 

150 

130 

85  to  105 

27.3 

402 

5883 

349 

5534 

13.7  + 

150 

to 

100 

27.3 

649 

8558 

343 

8310 

12.8 

152 

120 

95 

27.3 

766 

10062 

406 

9656 

12.6 

150 

100 

26.9 

956 

12858 

465 

12393 

12.95 

150 

105 

26.6 

1195 

16820 

453 

16367 

13.7 

About 

150 

Xone 

27.3 

245 

4765 

295 

4470 

18.2 

150 

" 

27.3 

406 

6628 

310 

6261 

15.4 

150 

117 

" 

27.3 

650 

9490 

347 

9175 

14.1 

150 

129 

( ( 

27.3 

716 

10488 

394 

10122 

14.1 

150 

138 

It 

26.3 

1144 

18015 

387 

17650 

15.4 

curves  plotted  in  Fig.  92.  The  turbine  was  of  400  K.AV.  rated 
capacity,  equipped  with  automatic  by-pass  valve.  Revolutions 
per  minute  3600.  The  results  are  intended  to  show  the  gain 
in  economy  due  to  the  use  of  superheated  steam.     It  is  to  be 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


253 


noted  that  the  vacuum  was  only  about  27  ijiches  of  mercury. 
The  power  wils  al)sorbe(l  by  a  water-Iirake. 


r  10 


Brake  Horse  Power 
100   200   300   400   500   COO   700   800   900   1000   1100   1200 


900   1000   1100 
B.H.P. 

Fig.  92. 


1300   1400 


1600 


The  table  on  page  252  gives  the  trial  results,  represented  in 
Fig.  92,  from  a  750-K.\V.  Parsons  turbine  running  at  1800 
revolutions  per  minute.  The  power  was  absorbed  b)'  a  water- 
brake.  The  results  are  intended  to  show  the  gain  in  economy 
obtained  by  increasing  the  vacuum  from  26"  to  28".  All 
the  tests  were  made  with  superheated  steam. 


^ 

(^ 


T 


256 


S  TEA  M-  T  URBINES. 


Gage  Pressure. 

Vacuum, 

Degrees 

Brake 
Horse- 

Steam  Consumption. 

Before 

After 

Inches. 

Superheat. 

Total 

Per  B.H.P. 

Entering 

Passing 

per  Hour. 

Hour. 

Throttle. 

Throttle. 

153 

62 

26 

150 

524 

8459 

16.04 

152 

108 

26 

146 

1025 

13516 

13.18 

150 

136 

26 

147 

1285 

16784 

13.14 

146 

122 

26 

142 

1586 

19938 

12.98 

152 

51 

28 

144 

520 

7194 

13.85 

149 

102 

28 

153 

1067 

12578 

11.79 

151 

125 

28 

152 

1346 

15368 

11.42 

150 

138 

£8 

153 

1530 

17623 

11.52 

The  essential  difference  between  the  impulse-  and  the 
reaction-turbines  is,  that  in  the  former  the  pressures  on  the 
two  sides  of  a  rotating  wheel  and  also  of  a  guide-wheel  are 


Fig.  95. — Blading  of  a  Westinghouse-Parsons  steam-turbine.    Rotor  only. 

equal  to  each  other,  or  are  supposed  to  be  in  the  ideal  case; 
in  the  latter  the  pressure  drops  from  the  entering  side  of  either 
a  guide  or  a  rotating  wheel,  and  thus  expansion  and  acceler- 


t^ 


TYPES  OF    TURBINE  AND    THEIR   OPERATION. 


259 


ation  of  the  jet  occur  in  each  row  of  blades.    In  the  simple 
impulse-turbine  a  set  of  nozzles  discharges  upon  the  buckets 


( 


Fig.  9S — Rotor,  complete,  with  balance-pistons,  Westinghouse-Parsons 

turbine. 


Fig.  99  — Bearing,  with  concentric  brass  sleeves,  Westinghouse-Parsons 

turbine. 


of  a  single  wheel.  In  the  compound  impulse-turbine  a  set 
of  nozzles  discharges  upon  a  series  of  mo\ing  and  stationary 
rows  of  buckets,  the  latter  changing  the  direction  from  the 


26(3  STEAM-TURBINES. 

former,  so  that  rotation  in  a  common  direction  is  produced  by 
the  action  of  the  steam  upon  each  moving  wheel.  The  dis- 
charge from  any  set  of  rotating  and  guide  wheels  may  be 
allowed  to  expand  through  a  second  set  of  nozzles,  or  orifices, 
and  the  resulting  jet  caused  to  act  upon  a  second  series  of 
rotating  and  guide  wheels.  The  same  process  may  be  repeated 
in  succeeding  stages,  to  as  great  an  extent  as  necessary  to 
absorb  as  much  as  possible  of  the  energy  of  the  steam. 

In  the  Parsons  turbine  as  applied  to  stationary  work, 
the  end  thrust  caused  by  the  axial  component  of  the  action 
of  the  steam  on  the  blades  is  neutraUzed  so  as  to  prevent 
the  spindle  moving  in  an  axial  direction,  by  balance-pistons, 
as  shown  at  P  in  Fig.  93.  These  are  grooved  at  the  periphery, 
and  mesh  with  corresponding  grooves  and  projections  on  the 
stationary  part  of  the  machine  so  as  to  prevent  leakage  of  the 
steam  past  them.  The  area  of  the  pistons  is  proportioned 
according  to  the  amount  of  thrust  which  they  are  required 
to  balance. 

For  the  low-pressure  cylinders  of  Parsons  turbines  the 
blades  become  quite  long,  and  in  order  to  give  them  sufficient 
stiffness  special  means  are  taken  for  holding  the  outer  ends 
of  the  blades.  The  Westinghouse  ^Machine  Company  employs 
for  this  purpose  a  special  form  of  wire  "  lacing,"  which  holds 
the  ends  of  the  blades  firmly.  The  recess  in  the  largest  blade 
shown  in  Fig.  102  is  for  recei\dng  the  stiff ening-strip  or  shroud- 
wire. 

In  the  turbines  for  the  large  Cunard  steamer  "  Carmania  " 
this  form  of  fastening  was  tried  first,  but  was  modified  because 
the  expansion  of  the  turbine  parts  required  that  the  ends  of 
the  blades  should  be  held  less  rigidly.  The  modification  con- 
sisted in  making  the  shroud-wire  in  sections,  and  joining  the 
ends  by  inserting  them  in  short  lengths  of  tubing,  flattened 
so  they  took  the  place  of  the  shroud-wire  at  certain  places  in 
the  circumference.  The  shroud-wire  was  thus  provided  with 
slip-joints,  as  the  ends  were  free  to  move  back  and  forth  in 
the  flattened  tubes. 


TYPES  OF  TURBINE  AND   THEIR  OPERATION. 


201 


In  Parsons  turbines  of  small  sizes  flexible  bearings  are 
used  in  order  to  permit  the  spindle  to  revolve  about  its  gravity 
instead  of  its  geometric  axis,  so  that  at  high  speeds  the  effect 
of  minute  errors  in  balancing  of  the  disks  may  be  neutrahzed. 
The  flexible  bearings  consist  of  several  concentric  bronze 
sleeves,  with  sufficient  clearance  to  allow  oil-films  to  form 
between  the  sleeves,  thus  permitting  the  shaft  to  vibrate  within 
narrow  limits.     In  all  machines  running  below  1200  revolu- 


FiG,  100.— Westinghouse-Parsons  governor  and  connections  to  controlling-valve. 

tions  per  minute,  however,  the  flexible  bearing  is  replaced  by  a 
solid  self-aligning  bearing. 

Water-sealed  packing-glands  are  used  at  the  ends  of  the 
casings  to  prevent  the  escape  of  steam  or  the  influx  of  air 
at  the  point  of  entry  of  the  shaft. 

Steam  enters  the  turbine  through  a  strainer,  thence  through 
a  poppet-valve  controlled  by  the  governor.  In  the  manner 
of  operating  this  valve,  practice  varies  among  the  different 
makers  of  Parsons  turbines.  As  made  by  the  Westinghouse 
Machine  Company,  the  poppet-valve  opens  and  closes  at  inter- 


262  STEAM-TURBINES. 

vals  proportional  to  the  speed  of  the  turbine.  At  light  loads 
the  valve  opens  for  short  periods,  remaining  closed  the  greater 
part  of  the  time.  As  the  load  increases  the  valve  remains 
open  longer,  until  when  full  pressure  is  continually  maintained 
in  the  high-pressure  end  of  the  turbine  the  valve  merely  vibrates 
without  sensibly  affecting  the  pressure  of  the  steam.  If  the 
load  on  the  machine  is  still  further  increased,  an  auxiliary 
poppet-valve  begins  to  open,  and  admits  steam  from  the 
throttle-valve  directly  into  the  lower  cylinders  of  the  turbine, 
increasing  the  total  power  developed.  The  economy  decreases 
with  the  opening  of  this  secondary  or  "  by-pass  "  valve,  but 
the  range  of  load  at  which  the  turbine  may  be  operated  with 
a  fair  degree  of  economy  is  very  greatly  extended.  The  inter- 
mittent action  of  the  valve  admitting  the  steam  is  accompanied 
by  a  constantly  reciprocating  motion  of  the  operating  mechan- 
ism, which  is  thereby  made  especially  sensitive. 

The  bearings  of  Parsons  turbines  are  supplied  with  oil 
under  pressure,  a  continuous  stream  being  circulated  by  an 
oil-pump  operated  from  the  main  shaft. 

The  Allis-Chalmers  Company  of  Milwaukee  has  recently 
entered  the  steam-turbine  field  with  a  turbine  of  the  Parsons 
type,  with  the  arrangement  of  blading  shown  in  Figs.  105  to 
107.  The  roots  of  the  blades  are  formed  in  dovetail  shape, 
and  inserted  in  slots,  cut  in  foundation-  or  base-rings,  the 
slots  conforming  to  the  shape  of  the  blade-roots.  The  foun- 
dation-rings are  of  dovetail  cross-section,  and  are  inserted  in 
dovetailed  grooves,  cut  in  the  turbine  spindle  and  cylinder 
respectively,  in  which  they  are  firmly  held  by  key-pieces. 
The  latter,  after  being  driven  into  place,  are  upset  into  under- 
cut grooves.  The  tips  of  the  blades  arc  protected  and  rein- 
forced by  a  shouldered  projection,  which  is  inserted  in  a  slot, 
punched  in  a  shroud-ring.  These  slots  are  so  punched  as  to 
produce  accurate  spacing,  and  at  the  same  time  to  give  the 
proper  angles  to  the  blades,  independent  of  the  slots  in  the 
base-ring.  After  insertion  in  the  slots,  the  blade-tips  are  riveted 
over. 


TYPES  OF   TLRBINE  AND   THEIR  OPERATION  263 

The  shroud-ring^  are  made  in  channel  shape,  with  thin 
projecting  flange^.  This  is  to  protect  the  ends  of  the  blades 
in  case  of  accidental  contact,  and  at  the  same  time  is  thought 
to  reduce  the  loss  by  leakage.  The  blading  is  put  in  place 
and  fastened  by  machinery. 

There  is,  in  this  t^'pe  of  Parsons  turbine,  a  special  arrange- 
ment of  balance-piston,  placed  in  the  low-pressure  end  instead 
of  in  the  high-pressure  end  of  the  turbine,  and  leakage  past 
it  is  prevented  by  what  is  called  a  labyrinth-packing,  consisting 
of  radial  baffles.  The  construction  and  general  arrangement 
of  the  turbine  is  shown  in  Figs.  103-107. 

The  meaning  of  the  word  "stage"  in  the  two  types  of  tur- 
bine has  been  variously  defined.  In  the  impulse-turbine  a  stage 
consists  of  a  set  of  nozzles  and  a  set  of  buckets  upon  which 
the  jet  from  the  nozzles  acis.  If,  as  in  the  case  of  the  Curtis 
turbine,  and  others  of  the  same  type,  the  discharge  from  the 
first  moving  buckets  is  guided  into  succeeding  mo\dng  buckets, 
in  order  to  absorb  further  the  kinetic  energy  wdiich  has  been 
produced  in  the  nozzles,  the  whole  combination  of  nozzles 
and  the  wheels  upon  which  the  jet  acts  is  called  a  stage.  If 
a  second  set  of  nozzles  be  added,  discharging  upon  one  or  more 
moving  wheels,  this  becomes  the  second  stage  of  the  turbine, 
and  so  on. 

In  the  Parsons  turbine,  since  the  stationary  or  guide 
blades,  in  one  row,  act  as  nozzles  for  the  succeeding  row  of 
moving  blades,  the  two  rows  taken  together  may  be  correctly 
called  a  stage.  Exception  has  been  taken  to  this,  upon  the 
g  ound  that  expansion  occurs  in  the  moving  as  well  as  in  the 
glide  blades,  and  it  has  therefore  been  suggested  that  each 
row  of  moving  blades  and  each  row  of  guide-blades  form 
a  complete  stage.  Throughout  this  book  the  word  stage,  as 
applied  to  the  Parsons  type  of  turbine,  means  a  row  of  guide- 
blades  and  a  row  of  moving  blades  taken  together. 

The  elements  upon  which  the  steam  acts  in  impulse-turbines 
are  commonly  called  buckets,  a  name  used  in  connection  with 
water-wheels.      In  turbines  of  the  Parsons  type  the  elements 


264 


STEAM-TURBIXES 


acted  upon  by  the  steam  are  of  (luite  different  shape,  and  of 
greater  length  than  those  in  the  impulse-turbine,  and  are  known 
as  blades,  or  sometimes  as  rones.  Fig.  102  shows  \arious  sizes 
of  blades,  as  used  in  Parsons  turbines;  and  on  page  163  are 
shown  outlines  of  the  buckets  used  in  the  Curtis  turbine. 


Fig.  101. — ^Westinghouse-Parsons  governor. 


The  Compound  Impulse-turbine.  —  The  best  known  tur- 
bine of  the  compound  impul.'^e  type  manufactured  in  this 
country  is  the  Curtis.  Figs.  109-118  show  general  arrange- 
ments and  structural  details  of  the  machine  as  manufactured 
by  the  General  Electric  Company. 

As  shown  in  Fig.  60  illustrating  the  500-K.W.  two-stage 
machine,  the  turbine  proper  is  divided  into  two  compartments,  in 
each  of  which  are  three  moving  bucket-wheels  and  two  rows  of 


•S- 

IS' 


266 


STEAM-TURBINES. 


stationary  buckets.  The  three  moving  wheels  in  each  stage 
are  firmly  bolted  together,  and  are  attached  to  a  single  hub 
mounted  upon  the  vertical  main  shaft  of  the  turbine.  Before 
entering  the  buckets  of  the  first  stage  the  steam  passes  through 


a  set  of  twelve  nozzles,  about  h  inch  diameter,  covering  a  sec- 
tion of  the  circumference  about  28  inches  in  length.  The 
clearance  between  the  edges  of  the  revolving  and  stationary 
buckets  is  about  jV  of  an  inch,  and  they  are  arranged  so  that 
there  is  no  possibiUty  of  bucket  interference. 


268 


STEA  M-TURBINES. 


The  nozzles  directing  the  steam  upon  the  buckets  of  the 
second-stage  wheels  are  placed  in  a  diaphragm  which  separates 
one  stage  from   the   other.    The   twelve  nozzles   of  the  first 


w^       a 


stage  are  divided  into  six  sets,  each  containing  two  nozzles, 
and  each  set  is  supplied  with  steam  through  a  single  vertical 
poppet-valve.  The  upper  end  of  the  valve  is  of  cyHndrical 
shape,   of  larger   diameter   than   the  valve  itself,   and   moves 


270 


STEAM-TURBINES. 


Fig.  107. — Allis-Chalmers  Turbine-blading. 


1  11     I  I  i  i  i  I    'I' 

I    LiJ*h.     I    §    I    t    /    I      fir 


Fig.  lOS. — Rotor  for  turbo-generator  (Allis-Chalmers  Co.). 


o 
o 
00 


W. 


C5 


272 


S  TEAM -TURBINES. 


up  and  down  in  a  vertical  cylinder.  The  valve  is  caused  to 
open  by  steam,  which  is  admitted  through  a  port,  opened 
and  closed  by  a  pilot,  or  "  needle,"   valve.    This  pilot-valve 


Fig.  llu.— 2000-K.W.  Curtis  turbine,  750  R.P.M.,  6600-volt  generator. 

is  actuated  by  an  electromagnet,  the  circuit  in  which  is  made 
and  broken  by  a  controlling  mechanism,  which  in  turn  is  actu- 
ated by  the  governor  at  the  extreme  upper  end  of  the  shaft. 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


273 


The  numl)or  of  valves  wiiich  iire  open,  and  the  length  of  time 
they  are    open,   control  the  steam-supply,  and  therefore   the 


Fig.  111.— 2000-K.W.  Curtis  turbine,  four-stage,  750  R.P.M..  6600-volt 
generator. 

power  of  the  turbine.  The  valves  which  are  operative  at  any 
one  time  are  always  either  full  open  or  completely  closed,  there 
being  no  intermediate  position. 


TYPES  OF   TURBINE  AND   THEIR  OPERATION.         21  o 


Fig.  113.— New  2000-K.\V.  60-cycle  turbine  and  generator. 


276 


STEAM-TURBINES. 


Surrounding  the  shaft,  above  the  first  stage,  and  at  the 
lower  part  of  the  second  stage,  are  packing-boxes,  which  pre- 
vent leakage    of  air   into    the    two  chambers  containing  the 


Fig.  114. — ^Tension-spring  governor  for  500-K.W.  Curtis  turbine. 

revolving  wheels.  There  are  two  carbon  rings  in  each  of 
these  packing-boxes,  which  fit  the  shaft  and  the  top  and  bot- 
tom of  the  packing-box  closely.    The  space  between  the  rings 


TYPES  OF   TURBINE  AND    THEIR  OPERATION. 


277 


is  filled  with  steam,  at  a  i)ressure  slightly  above  that  of  the 
atmosphere.  If  any  leakage  should  occur  ])ast  the  lower  ring 
of  the  first-stage  j)acking,  or  i)ast  the  u|)i)er  ring  of  the  second- 
stage  packing,  steam  would  flow  in  and  prevent  the  entrance 
of  ail'  into  the  turbine. 


Fig.  11.5. — Buckets  on  one  of  the  wheels  of  a  500-K.W.  Curtis  turbine. 


The  lower  end  of  the  shaft  is  supported  by  a  cast-iron  step- 
bearing,  which  takes  the  weight  of  the  turbine  and  generator. 
This  bearing  is  kept  continually  suppHed  with  lubricating- 
oil  under  pressure,  which  is  maintained  by  a  .'^mall  electric 
pump,  mounted  on  the  base  of  the  turbine.     An  accumulator 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


279 


is  arranged,  so  that  if  the  pump  should  break  down,  the  supply 
of  oil  would  be  automatically  continued. 

When  it  is  desired  to  run  the  turbine  non-condensing,  the 
exhaust  is  carried  away  from  the  first  stage  of  the  turbine 
through  an  atmospheric  vent-pipe,  fitted  with  an  automatic 


Fig.  117. — 75-K.W.  Curtis  turbine-wheels,  assembled  in  wheel-casing. 
Upper  half  of  casing  removed. 


relief-valve.     The   second-stage   nozzles  may  be  shut  ofT  by  a 
valve,  when  the  turbine  is  to  operate  non-condensing. 

In  the  supply-pipe  is  an  automatically  operated  butter- 
fly valve,  arranged  to  cut  off  the  steam-supply  in  case  the 
speed  of  rotation  becomes  too  high.  A  strainer  is  located 
between   the   throttle- valve   and  the  steam-chest,   to  prevent 


280 


STEA  M-TURBINES. 


the  entrance  of  any  solid  matter  that  might  injure  the  work- 
ing parts  of  the  turbine. 

The    table    of    results   of    Curtis    turbine  tests  shows  the 
economy  attained  with  the  use  of  two-stage  turbines  at  the 


Fig.   118.— Rotating  parts  of  25-K.W.,  3600  R.P.M.,  Curtis  turbine, 
non-condensing. 


Newport  Station  of  the  Old  Colony  Street  Railway  Com- 
pany (see  pages  282-3).  The  tests  were  made  by  Mr.  George 
H.  Barrus.  Upon  the  basis  of  these  results  he  makes 
the  following  comparison  between  the  economy  of  the 
turbine  and  that  of  the  direct-connected  reciprocating  steam- 
engine. 

Taking  the  efficiency  of  the  engine  installation  as  85  per 
cent,  that  is,  Elec.  H.P. -^I.H.P,  =0.85,  for  high-class  com- 
pound steam-engines  the  consumption  of  dry  steam  may 
be  taken  as  13-^0.85  =  15.3  pounds  per  E.H.P.  hour.  The 
turbines  tested,  at  full  load,  consumed  14.7  pounds  per  E.H.P. 
Thus  the  turbine  was  4  per  cent  more  economical  at  full  load 
than  a  first-class  compound  reciprocating-engine,  direct-con- 
nected. At  half  load  the  reciprocating-engine  consumes  14.5 
pounds  per  I.H.P.  hour.  The  efficiency  of  the  generator  at 
half-load  is  0.70,  or  the  steam  consumption  is  14.5  ^  0.70  =  20.7 
pounds  per  E.H.P.  hour.  The  turbine  consumed  15.9  pounds 
per  E.H.P.  hour;    or,  effected  a  gain  of  23  per  cent. 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


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282 


STEAM-TURBINES. 


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■Po-sP  =  «-'Ec-'? 


-^  .   i  --  ,-1=  s* 


■S-s-S  S-. 


Ji  «  i_   O  u        O 

t)  ffi  p  o;  ^  3-  0) 
3030-3 


•-"Nco*     incot-     X     OS     c     —c^x     CO     -*ic;Dt>-     x 


284  STEAM-TURBINES. 

Continuing,  Mr.  Barrus  says:  "The  coal  consumption  on 
Jan.  15  was  2.54  pounds  dry  coal  per  K.W.  hour  of  total  out- 
put. If  this  test  had  been  made  with  furnace  efficiency  as 
high  as  has  been  obtained  with  these  boilers,  the  figure  would 
have  been  2.29  pounds  of  coal.  There  was  an  abnormal  loss 
of  steam  between  JDoilers  and  turbine,  being  14.8  per  cent  and 
16  1  per  cent.  In  good  practice  this  should  not  be  over  7.5 
per  cent.  Allowing  for  such  a  loss,  the  coal  consumption 
would  be  2.12  pounds  per  K.W.  hour,  or  1.58  per  E.H.P.  hour. 
Compared  with  power-station  practice,  this  figure  should  be 
converted  to  switchboard  output,  and  coal  slightly  wet.  Allow- 
ing for  current  used  by  condenser  auxiliaries,  as  14.9  K.W., 
and  for  4  per  cent  moisture  in  coal,  the  consumption  of 
wet  coalper  K.W.  hour  of  switchboard  output,  in  good 
practice  under  these  circumstances  (the  average  net  load  be- 
ing 407  K.W.),  becomes  2.29  pounds.  With  corresponding 
high-class  reciprocating-engine  stations,  the  coal  consumption 
per  K.W.  hour,  of  switch-board  output,  is  from  2.5  to  2.6 
pounds. 

''These  tests  were  made  with  two-stage  turbines,  and  fur- 
ther economy  may  be  expected  from  tm-bines  with  a  larger 
number  of  stages. 

''The  advantage  of  superheating  revealed  by  the  Newport 
tests,  on  coal  basis,  is  only  4.4  per  cent  under  the  most  favor- 
able conditions  of  temperature  and  efficiency.  This  result 
was  obtained  with  a  temperature  of  700°  at  the  superheater. 
There  is  good  reason  for  expecting  that  increasing  the  number 
of  stages  of  the  turbine  will  be  attended  by  a  proportional 
gain,  due  to  superheating,  over  the  ,two-stage  machine.  What- 
ever percentage  of  sa\dng  in  steam  consumption  may  thus 
be  secured,  there  will  be  the  same  percentage  of  increase  in 
coal  economy,  and  the  improvement  will  be  clear  gain." 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


285 


Economy  of  Turbine  expressed  in  Heat-units  per 
Electrical  Horse-power. 

The  B.T.U.  per  E.H.R  hour  were  16,923,  at  full  load, 
with  saturated  steam,  and  15,012  with  289.6°  superheat  (using 
0.48  as  the  specific  heat  of  superheated  steam).  The  heat 
utilized  in  evaporation  per  pound  of  dry  coal  was  10,765 
B.T.U.  On  this  basis  the  above  figures  represent  a  con- 
sumption of  1.57  pounds  dry  coal  per  E.  H.  P.  hour  for 
saturated  steam,  and  1.39  pounds  for  superheated  steam  per 
E.H.P.  hour.  The  heat  consumptions  given  are  equivalent 
to  282  B.T.U.  per  E.H.P.  per  minute  for  saturated  steam,  and 
250  for  superheatetl  steam. 

The  comparisons  given  above,  between  the  performance  of 
turbines  and  compound  reciprocating-engines  are  based  upon 
the  results  of  one  particular  type  of  turbine,  because  the 
figures  were  at  hand,  but  any  of  the  well-developed  types 
would  give  approximately  the  same  results  under  similar 
conditions. 

The  turbine,  although  possessing  distinct  advantages  in  point 
of  convenience,  space,  oil  and  attendance  required,  has  not 
yet  equaled  the  steam  economy  attained  with  the  best  triple- 
expansion  stationary  reciprocating  engines.  A  comprehensive 
comparison  places  the  two  types  of  motor  very  close  together 
in  general  utiUty  and  effectiveness,  with  the  turbine  gaining 
ground  for  power  station  service  because  of  its  simplicity. 

Fig.  113  shows  one  of  the  latest  designs  of  Curtis  turbine, 
having  four  stages  and  rated  capacity  2000  K.W.  The  results 
in  the  following  table  are  from  a  test  made  at  Schenectady  in 


FuU  Load. 


Half  Load. 


Quarter 
Load. 


No  Load. 


Duration  of  test,  hours 

Steam-pressure,  gage 

Back  pressure,  inches  mercury.  .  . 

Superheat,  degrees  F 

Load  in  kilowatts 

Steam  per  kilowatt  hour,  pounds . 


1.25 
166.3 
1.49 
207 
2023 . 7 
15.02 


0.916 
170.2 

1.40 

120 
1066.7 
16.31 


1.00 
155.5 
1.45 
204 
555 
18.09 


1.33 
154.5 

1.85 

153 

1510.5* 


*  Total  water  per  hour. 


286  STEAM-TURBINES. 

1905,  under  the  direction  of  Messrs.  Sargent  and  Lundy  of 
Chicago.    The  revolutions  per  minute  were  900. 

In  Figs.  116  to  118  are  shown  small  horizontal  Curtis  tur- 
bines, direct-connected  to  generators.  The  latter  are  direct- 
current  machines  and  operate  at  the  speeds  of  revolution  given 
in  the  table  on  page  287. 

Other  t3rpes  of  turbine  are  about  to  be  introduced  in  this 
country,  similar  to  the  output  of  European  firms.  The  Hooven- 
Owens-Rentschler  Company  of  Hamilton,  Ohio,  is  building 
the  Hamilton-Holzwarth  turbine,  which  is  of  the  general  char- 
acter of  the  Rateau  turbine,  operating  upon  the  impulse  prin- 
ciple entirely,  and  having  several  compartments,  each  con- 
taining a  rotating  wheel. 

The  Zoelly  turbine,  also  of  the  many-stage  impulse  type, 
is  being  manufactured  by  the  Providence  Engineering  Works, 
of  Providence,  R.  I. 

Capacity  and  Speed  of  Revolution  of  Turbines. — The  follow- 
ing tables  give  particulars  of  Parsons  and  of  Curtis  turbines, 
as  built  for  operating  electric  generators. 

PARSONS  TURBINES. 

T^^  R.P.M.       R.P.M. 

■'*■•"•  60-cycle.      25-cycle. 

300 3600  1500 

400 3000       

500 3600  1500 

750 1800  1500 

1000 1800  1500 

1500 1200  1500 

2000 1200  1500 

3500 720  750 

5000 720  750 

6000 720  750 

7500 720  750 

200  K.W.  direct-current,  1850  R.P.M. 

The  speed  of  revolution  of  De  Laval  turbine  generators  is 
given  in  the  tables  of  tests.  The  speed  of  revolution  of  the 
turbine-wheel  is  usually  ten  times  that  of  the  generator  arma- 
ture. 


TYPES  OF   TURBINE  AND   THEIR  OPERATION. 


287 


CURTIS  TURBINES. 

DIRECT-CURKENT. 


Horizontal  Shaft. 


Class. 

Poles. 

K.W. 

R.P.M, 

Volts. 

c 

2 

15 

4000 

80-125 

( < 

2 

25 

3600 

125-250 

( ( 

4 

75 

2400 

125-250 

<  ( 

4 

150 

2000 

125-250 

<  t 

4 

300 

1500 

125-550 

Vertical  Shaft. 


Class. 

Poles. 

K.W. 

R.P.M. 

Volts. 

c 

4 

500 

1800 

550 

ALTERX.\TIXG-CURRENT. 


Vertical  Shaft — 60-cycle. 


Class. 

Poles. 

K.W. 

R.P.M. 

Volts. 

ATB 

4 

300 

1800 

240-  4000 

4 

500 

1800 

240-  6600 

6 

1000 

1200 

480-  6600 

8 

1500 

900 

480-  6600 

8 

2000 

900 

1150-13200 

12 

3000 

600 

600-13200 

10 

5000 

720 

2300-13200 

25-cycLE. 


Class. 

Poles. 

K.W. 

R.P.M. 

Volts. 

ATB 
tt 

2 
2 
4 
4 

300 

800 

2000 

5000 

1500 

1500 

750 

750 

370-  6600 

600-13200 

2300-13200 

2300-13200 

288 


STEAM-TURBINES. 


Clearances  in  Turbines.  —  In  impulse-turbines  fitted  with 
guide-buckets  the  clearance  between  buckets  is  important; 
but,  as  was  shown  in  the  experimental  work  described  in  Chap- 
ter VI,  small  clearances,  such  as  are  necessary  for  mechanical 
operation  of  the  wheels,  do  not  seriously  affect  the  efficiency. 
The  following  clearances  are  recommended  by  the  General 
Electric  Company* 


Turbine. 

Clearances. 

Rating. 

Stages. 

First  Stage. 

Second  Stage. 

Third  Stage. 

Fourth  Stage. 

500 

4 

0 . 06  inch 

0.06  inch 

0.06  inch 

0 . 06  inch 

800 

4 

.07    " 

.07    " 

.07     " 

.07    " 

1000 

7 

.08     " 

.08     " 

.08     " 

.15     " 

1500 

4 

.06    " 

.06    " 

.06     " 

.08     " 

2000 

4 

.06     " 

.06    " 

.08     " 

.08     " 

3000 

4 

.07     " 

.07    " 

.07     " 

.08     " 

5000 

4 

.07    " 

.07    " 

.07     " 

.08     " 

5000 

6 

.10     " 

.1       " 

.1       " 

.2       " 

In  the  ideal  many-stage  turbine,  since  there  is  no  drop  in 
pressure  in  any  given  stage  after  the  steam  leaves  the  nozzles, 
the  direction  of  flow  is  determined  by  the  nozzles  and  guide- 
buckets,  and  the  clearance  past  the  periphery  of  the  wheels  is 
of  little  or  no  consequence.  A  certain  amount  of  clearance  is 
desirable  from  mechanical  considerations,  and  this  apparently 
does  not  interfere  with  the  efficiency  of  the  actual  machine. 

In  the  reaction  type  of  turbine  it  is  the  limitation  of  clear- 
ance past  the  periphery  of  the  blades  that  is  important,  and 
not  that  between  the  rows  of  blades.  This  is  because  there  is 
expansion  of  the  steam  all  along  the  turbine,  and  the  steam 
tends  to  flow  in  all  directions.  Leakage  past  the  ends  of  the 
blades  is,  therefore,  to  be  prevented,  and  the  clearances  are 
kept  as  small  as  possible.  Knowledge  regarding  the  expansion 
of  the  spindle  and  casing  caused  by  the  temperatures  attained 
in  operation  is  possessed  by  turbine-builders,  and  the  clear- 
ances are  arranged  accordingly.     The  clearances  between  rows 


*  See  Report  of  Committee  for  the  Investigation  of  the  Steam-turbine, 
National  Electric  Light  Assoc,  June,  1905. 


TYPES  OF  TURBINE  AND   THEIR  OPERATION.         289 

of  blades  vary  from  i  or  rs  inch  in  the  liigh-pressuie  stages  to 
one  inch  or  even  more  in  the  lower-pressure  stages.  The  clear- 
ance between  the  tips  of  the  blatles  and  the  casing  or  spindle, 
as  the  case  may  be,  is  limited  to  a  few  one-thousandths  or  a 
few  one-hundredths  of  an  inch,  according  to  circumstances. 

The  gain  due  to  increase  of  vacuum  is  illustrated  by  the 
following  extract  from  the  "Report  of  the  Committee  for  the 
Investigation  of  the  Steam-turbine,"  appointed  by  the  National 
Electric  Light  Assoc,  and  before  referred  to: 

''From  a  recent  test  made  by  your  committee  on  a  2000- 
K.W.  turbine,  different  vacua  were  run  for  the  specific  purpose  of 
obtaining  the  vacuum  effect ;  it  was  found  that  for  this  turbine 
running  at  ISOO  kilowatts  the  increase  in  economy  is  5.2  per 
cent  from  2j-inch  to  27-inch  vacumn,  and  6.75  per  cent  from 
27-inch  to  28-inch. 

"Under  the  following  assumed  conditions  the  economy 
effected  in  operating  under  high  vacuum  would  w^ork  out  some- 
what as  follows : 

Assumed  size  of  unit,  K.W 2000 

Average  load 1500 

Hours  run  per  day 15 

Hours  run  per  year  (300  days) 4.500 

Price  coal  per  ton,  2000  pounds S3 .00 

Evaporation 9  pounds 

Economy  pounds  water  per  kilowatt 22 

Rise  in  vacuum 26-28  inches 

Assumed  per  cent  increase  of  economj^  due  to 

increase  of  vacumn  from  26-28  inches 6  per  cent 

Water  saved  per  K.W.-hour 1 .32 

Water  saved  per  year 1-40,000  cu.  ft. 

Cost  of  water  saved  per  year  at  2.58 $35.00         $35.00 

Coal  saved  per  year 500  tons 

Cost  of  coal  saved  per  year  at  .S3 .  00 $1 500 .  00     $1 500 .  00 

$1535.00 

Increased  cost  of  condenser  plant  for  28-inch 

over  that  of  26-inch  assumed  S5000. 00;  in- 
terest on  above  at  5  per  cent,  depreciation 
10  per  cent,  other  fixed  charges,  including 
repairs,  2  per  cent,  total  17  per  cent SS50 .00         850 .00 

Sa^•ing  per  year $685.00 


290  STEAM-TURBINES. 

Saving  per  year 5685.00 

The  above  does  not  include  the  extra  cost  in  steam 
to  run  the  larger  auxiliaries,  but,  inasmuch  as 
such  exhaust-steam  would  return  a  benefit  to 
the  feed-water  if  they  were  all  steam-driven,  we 
will  assume  that  the  extra  cost  in  water  is  2  per 
cent  of  the  total  steam  guaranteed  by  the  turbine 
and  will  amount  per  year  to $12.00  12.00 

Total  net  saving $673 .00 

With  interest  at  5  per  cent  this  represents  a  capital 

saving  of 13,460 .00 

Sizes  of  Condensers  and  Auxiliaries. — ''The  turbine  instal- 
lations concerning  which  we  have  received  information,  where 
28  inches  of  vacuum  is  maintained  with  a  coohng-water  tem- 
perature of  70  degrees  F.,  show  a  miniumm  ratio  of  cooling 
surface  in  the  condenser  to  steam  condensed,  per  minute,  of 
6.9  scjuare  feet  per  pound.  But  the  more  usual  ratio,  even 
where  the  cooling  water  is  from  5  to  10  degrees  lower  in  tem- 
perature, is  8  to  9  square  feet  per  pound.  In  the  first  instance 
noted  above  it  is  to  be  remarked  that  the  ratio  of  circulating 
water  to  condensed  steam  is  70  to  1.  With  greater  coohng 
surface  ratios  the  proportion  of  cooling  water  is  reduced. 

"In  actual  practice,  for  temperatures  of  cooling  water  rang- 
ing from  60  to  70  degrees,  circulating-pumps  have  been  installed 
for  volumes  of  cooling  water  ranging  from  40  to  70  times  that 
of  the  water  of  condensation.  At  the  low  ratio  of  40  to  1  the 
cooling  water  temperature  must  be  close  to  60  degrees  for  so  high 
a  vacuum  as  27.5  inches,  and  even  then  considerable  difficulty  is 
experienced  in  maintaining  the  27.5  inches,  unless  the  ratio  of 
cooling  surface  to  pounds  of  steam  condensed  per  minute  is  8  to  1. 

Steam  Used  by  Auxiliaries.  —  ''These  figures  are  obtained 
from  letters  sent  to  us  by  turbine  owners: 

3  200-K.W.  De  Laval  exhausting  into  one  condenser. 

3000  gallons  per  minute  circulating-pump;  2-stage  dry- 
vacuum  pumps  8X12  X|f;  duplex  wet-vacuum  pump;  15-K.W. 
turbine  exciter.     Steam  by  auxiharies,  2.6  pounds  per  kilowatt. 

Byllesby  &  Co. : 

Steam  per  kilowatt  at  half  load,  3.5  pounds. 


TYPES  OF   TURBINE  AXD   THEIR  OPERATION. 


291 


Boston  Edison  Company. 

5000-K.W.  Turbine  Unit. 

Kilowatts  on  turbine 2713          3410           4758 

Vacuum 28 . 4 

Barometer 29 .  53 

Boiler-feed  pump,  I.H.P 13.9 

Circulating-pump,  I.H.P 69.1 

Dry-vacuum  pump,  I.H.P 24.3 

Step-bearing  pump,  I.H.P 6.4 

Wet-vacuum  pump,  E.H.P 8.6 

Total  power  for  auxiliaries 122.3 

Per  cent  of  power  of  auxiliaries  to  power  of 

turbine 3.4            2.9            2.1 

Per  cent  of  water  used  by  auxiliaries  to  that 

used  by  turbine 8.4            7.4            5.7 


28.7 

28.6 

29.95 

29.96 

23.7 

27.4 

69.1 

69.1 

23.2 

23.8 

5.8 

5.6 

9.2 

9.8 

131 

135.7 

Test  Reported  by  Nashua  Light,  Heat,  and  Power  Company. 
500-K.W.  Curtis,  Rated  Water  per  Hour  20.5  Pounds. 


Steam 
per  Hour, 
Satu- 
rated. 

Steam 
per  Hour, 
Super- 
heat. 

Pounds 
Differ- 
ence p)er 
Hour. 

One 
Per  Cent 
Differ- 
ence. 

Degrees 
Super- 
heat. 

Accimiulator-pump.  . 

Drj'-air  pump 

Boiler-feed  pump.  .  .  . 

W^estinghouse       jun. 

driving  circ.  pumps. 

130.9 

181.58 

352.15 

663.64 

130.9 
183.13 
249. 5S 

439.36 

102.57 
224.28 

29.12 
33.79 

71.98 
97.65 

Feed  pimips 
act  as  wet- 
vacuum 

Totals 

1328  27 

1002  97 

Per  cent  of  rated  water  consumption  of  turbines 

at  full  load 12.9  per  cent,  9.78  per  cent 

Dry-air  pump,  6"  and  12"  by  12"  stroke,  93  R.P.M. 
Boiler-feed  pumps,  7.5"  and  4.5"  by  10"  stroke,  98  R.P.M. 
Centrifugal-pump  engine,  7"  by  6"  stroke. 


"It  is,  however,  a  question  whether  the  extra  cost  of  steam 
for  driving  larger  aiixiharies  for  high  vacuum  work  is  of  any 
great  moment,  as  such  steam  is  of  considerable  value  in  the 
feed-heater.  It  is  to  be  noted  also  that  these  figures  are  for 
total  consumption  of  auxiUaries,  and  that  the  increase  of  steam 


292  STEAM-TURBINES. 

necessary  to  obtain  two  inches  more  than  26  or  28  inches  must 
necessarily  be  very  small. 

"An  important  featm'e  of  operation  with  high  vacuum  is 
the  necessity  of  having  air-tight  stuffing-boxes  and  pipe-joints, 
lack  of  which  results  in  loss  of  economy  to  the  turbine,  and 
increased  consumption  of  steam  by  the  dry-vacuum  pumps  and 
circulating  pumps. 

"Undoubtedly  th?  best  arrangement  of  the  condensing 
plant  is  the  use  of  a  counter-current  condenser,  placed  as  close 
to  the  exhaust-nozzle  as  possible  and  with  the  dry-air  pumps 
drawing  from  the  condenser  at  the  point  of  coolest  circulating 
water;  this  pump  also  so  placed  that  the  minimum  of  pipe  con- 
nection can  be  used.  With  this  arrangement  the  possibihty  of 
air-leaks  would  be  greatly  reduced,  the  quantity  of  circulat- 
ing water  would  also  be  lessened,  owing  to  the  lower  tension 
of  the  air  which  has  just  left  the  coldest  tubes  of  the  con- 
denser. We  believe  that  it  is  important,  in  lowering  operat- 
ing costs,  that  the  above  design  of  the  installation  should 
in  all  cases  be  followed  as  rigidly  as  individual  conditions 
will  permit. 

"From  the  experience  obtained  in  their  own  plants  and  in 
testing  others,  the  committee  recommends  that  the  capacity  in 
cubic  feet  of  volume  swept  by  the  air-piston  of  the  dry-air 
pump  be  not  less  than  45  times  the  volume  of  the  condensed 
steam;  and  where  overload  conditions  are  frequent,  not  less 
than  50  times  the  water  (condensed  steam)  volume." 

General  Remarks  on  Steam-turbine  Design. — The  experi- 
mental work  on  buckets,  discussed  in  Chapter  VI,  indicates  that 
the  placing  of  a  number  of  rows  of  moving  and  stationary 
buckets  in  a  single  stage  of  an  impulse- turbine  may  lead  to  an 
accumulation,  or  backing  up,  of  pressure.  This  may  be  caused 
by  any  of  the  following  conditions: 

(a)  Insufficient  area  for  the  passage  of  steam,  especially  in 
the  last  wheels  of  the  stage. 

(6)  Discharge  side  of  the  buckets  making  too  small  an  angle 
with  the  direction  of  motion  of  the  buckets. 


TYPES  OF  TURBINE  AND   THEIR  OPERATION.         293 

(c)  Bucket  surfaces  opposing  undue  frictional  resistance  to 
the  passage  of  steam. 

(d)  The  steam-passages  from  one  wheel  to  another  being 
indirect  and  opposing  undue  obstruction  to  the  fiow  of  steam. 
If,  in  order  to  reach  a  succeeding  row  of  buckets,  the  steam  has 
to  traverse  the  surface  of  a  rotating  wheel,  this  may  interfere 
with  free  flow  antl  cause  loss. 

These  conditions  may  prevent  the  production  of  the  desired 
rotative  effort  in  the  stage  in  question,  and  thus  call  for  modi- 
fications in  the  area  and  character  of  steam-passages,  in  the 
bucket  exit  angles,  and,  assuming  it  to  be  practicable,  in  the 
degree  of  smoothness  to  which  the  bucket  surfaces  are  finished. 

In  one  of  the  most  recent  types  of  Curtis  turbine  there  are 
four  stages,  and  one  rotating  disk  or  wheel  in  each  stage,  car- 
rying two  rows  of  buckets.  The  2000-K.W.  turbine  shown  in 
Fig.  113  is  of  this  type. 

In  general,  as  great  freedom  as  possible  is  required  for  pas- 
sage of  the  steam  through  the  high-pressure  stages  of  the  tiu-- 
bine.  But,  at  the  same  time,  sufficient  area  of  buckets  must 
be  provided  for  the  steam  to  act  against,  and  this  may  call  for 
an  increased  number  of  buckets  in  the  last  wheels  of  a  stage, 
as  the  exit  angles  are  increased. 

In  the  Parsons  type  freedom  of  steam-passage  is  equally  de- 
sirable, and  in  general  the  requirements  are  similar  to  those  just 
stated.  It  is  desirable  to  keep  the  steam  velocities  low,  and, 
while  certain  undesirable  features  appear,  it  is  quite  possible  to 
design  a  reaction-turbine  having  practically  uniform  steam 
velocities  throughout  the  machine. 

In  conclusion  it  should  be  said  that  the  determination  of 
sizes  and  general  proportions  of  mechanical  devices  of  all  kinds, 
and  more  especially  in  cases  of  departure  from  the  beaten  path 
such  as  that  now  being  made  by  the  builders  of  steam-turbines 
of  the  various  types,  is  only  a  first  step  towards  bringing  forth 
satisfactory  results  as  viewed  from  an  engineering  standpoint. 
The  development  of  satisfactory  details  and  the  commercially 
successful  production  of  the  finished  machine  call  for  technical 


294  STEAM-TURBINES. 

and  mechanical  skill  combined  with  business  ability  all  of  the 
highest  order,  and  unstinted  credit  is  due  to  the  men  who  have 
worked  and  are  working  to  perfect  the  mechanism  of  the  steam- 
turbine. 

Note  regarding  the  Design  of  Condensers  and  Air-pumps. — In 
a  paper  presented  to  the  Inst,  of  Naval  Architects,  London, 
Apr.  1906  (see  reprint,  ''Engineering,"  Apr.  13-20),  Prof.  R.  L. 
Weighton  describes  very  complete  experimental  work  performed 
in  order  to  ascertain  the  relative  efficiencies  of  the  surface  con- 
denser as  ordinarily  built  for  both  stationary  and  marine 
work,  and  the  surface  condenser  to  which  the  name  ''Contraflo" 
has  been  given.  The  conclusions  are  of  exceptional  interest, 
and  indicate  that  condensers  and  air-pumps  are  commonly 
made  of  considerably  greater  size  and  capacity  than  w^ould  be 
found  either  necessary  or  desirable  if  the  principles  brought  out 
in  the  paper  were  made  use  of  in  the  design  of  those  parts. 

The  type  of  counter-current  condenser  referred  to  on  page 
292  is  a  horizontal  surface  condenser,  in  which  the  cooling 
water  and  the  exhaust  steam  enter  in  opposite  directions,  pref- 
erably with  the  steam  entering  at  the  bottom  of  the  shell,  and 
the  water  through  the  tubes  at  the  top.  The  dry  air-pump  is 
then  caused  to  draw  from  a  connection  at  or  near  the  top  of 
the  condenser  shell. 


CHAPTER  X. 

THE  MARINE  STEAM-TURBINE. 

The  recent  decision  of  the  Cunard  Steamship  Company, 
and  that  of  the  British  Admiralty,  to  install  turbines  in  place 
of  reciprocating-engines  in  various  large  and  important  vessels, 
have  brought  the  marine  steam-turbine  very  prominently  before 
the  public.  This  departure,  made  by  conservative  engineers  who 
had  access  to  all  the  existing  data  on  the  subject,  has  apparently 
been  justified  by  the  subsequent  good  behavior  of  the  turbines 
already  installed.  The  question  as  to  the  efficiency  of  the  marine 
turbine  must  rest  upon  the  results  of  tests  of  different  classes  of 
vessels  under  various  conditions,  but  the  trials  made  thus  far  are 
very  gratifying  in  their  results,  and  cover  a  fairly  wide  range  of 
vessels,  from  the  first  small  boat,  Turbinia,  of  32  knots  speed, 
to  the  ocean  liner  Carmania,  of  about  19  knots  speed,  which 
has  just  completed  her  initial  voyage  successfully;  and  includ- 
ing the  third-class  cruiser  Amethyst,  in  which  the  economy 
of  the  turbine,  at  the  highest  powers,  exceeded  that  of  the 
reciprocating-engine  by  as  much  as  40  per  cent,  and  excelled 
in  eflSciency  at  all  speeds  above  14  knots  per  hour. 

The  following  table  gives  particulars  of  practically  all  of  the 
vessels  which  have  been  equipped  with  turbine  machinery. 

295 


296 


STEAM-TURBINES. 


TURBINE  STEAMERS— 
(The  table  is  from  a  paper  by  Mr.  E.  M.  Speakman, 


Date. 


1894^ 
1900 

1901 

1898 

do 

1903 


711904 
1905 

do 


do. 

1903 
do. 

do. 
1905 
do 
do. 
do 
1903 

do. 

1904 

do. 

do. 

1905 

do 

do 

do 
do 

do. 
do 


Vessel. 


Turbinia 

King  Edward.  . .  ■ 

Queen  Alexandra 

Viper 

Cobra 

Velox 

Eden 

Coastal  Destroy- 
ers.. 

Ocean-going  De- 
stroyers. 


Experimental 
Destroyers. 

Tarantula 

Loreua 

Emerald 

Albion 

Narcissus 

Royal  Yacht.  . 
Mahroussah.  . 
The  Queen  .  .  . 

Brighton 

Princess  Maud 

Londonderry.  . 

Manxman.  .  . . 

Viking 

Onward 

Dieppe 

Princess  Elizabeth 
Kaiser 


Service. 


Experimental   . .  . 
Pleasure  Steamer 

do 

T.  B.  D 

do 

do 

do 

do 

do 

do 

S.  Y 

do 

do 

do 

do 

do 

do 

Channel  Steamer 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 

do 


Owner. 


C.  A   Parsons 

Turbine  Steamers,  Ltd. 


do. 


R.  N. 
do., 
do.. 


do. 
do. 


do. 


do. 


W.  K.  Vanderbilt. 
A.  L.  Barbour.  .  .  . 


Sir  C.  Fumess 

Sir  G.  Newnes 

A.  E.  Mundy 

H.  M.  King  Edward.  .  . 
The  Khedive  of  Egypt, 
S.  E.  &  Chatham  Ry.Co, 

L.  B.  &  South-Coast 
Ry.  Co. 

Stranraer  &  Lame  Ser- 
vice. 

Midland  Railway  Co. .  . 


do 

Isle  of  Man  S.  S.  Co. 


S.  E.  <Sr.  Chatham  Ry. 

Co. 
L.  B.  &  S.-Coast  Ry.  Co. 


G.  &  J.  Burns 

Great  Western  Ry.  Co 


Belgian  Government. . 
Hamburg  -  Heligoland 
S.  S.  Co. 


Builder. 


C.  A.  Parsons. 
Denny  Bros.  .  , 


do. 


Hawthorn,  Leslie 
&Co. 

Armstrong,  Whif- 
worth  &  Co. 

Hawthorn,  Leslie 
&Co. 

do 

Thorn ycroft,  Yar- 
row and  White. 

Laird,  Thorny - 
croft,  A  r  m  - 
strong.  White, 
Hawthorn,  and 
Leslie  &  Co. 


Yarrow 

Ramage   &    Fer- 
guson. 
Stephen  &  Sons . , 
Swan  &  Hunter. . 

Fairfield 

A.  &  .T.  Inglis.  .  .  , 
do.  (rebuilding).  . 
Denny  Bros 


do. 
do. 
do. 


Vickers,  Sons  & 
Maxim. 

Armstrong,  Whit- 
worth  &  Co. 

Denny  Bros 


Fairfield. 


do 

J.   Brown   &   Co., 
and  Laird  &  Co. 

Cockerill 

Vulcan  Co 


*  Rebuilt  1896. 

Remarks. — ■]    Only  one  screw,  28"  diameter,  now  fitted  to  each  shaft. 

2.  Put  in  service  July,  1901. 

3.  Put  in  service  July,  1902.     Very  largely  used  for  experimental  trials. 

4.  Launched    6/9/99.       Ran    ashore    and    lost   during   naval   manoeuvres    in    1901. 
Trials  made  in  1 900. 

5  Sank  at  sea  in  September,  1901. 

6  Reciprocating  cruising  engines  on    inner  shafts,  7i",   11",  and   16"X9"  stroke; 
400  R  P.M.     Launched  2/1902. 

8.   Twelve  building. 
9    Five  building. 

10  Details  under  consideration 

11  One  3  0'   screw  now  fitted  to  each  shaft. 


THE  MARINE  STEAM-TURBINE. 


297 


■nEXERAL  DIMENSIONS  AND  DATA. 

Transactions  of  the  Inst,  of  Engineers  and  Shipbuilders  of  Scotland,  1905.) 


100 
250 

270 

210 

223 

210 

220 
175 

250 


320 

152  6 
253 

198 
270 
245 
310 
400 
310 

280 

300 

330 

330 

350 

310 


340 
350 


350 
300 


Beam 

J3 
1 

9 

'      " 

3 

30 

10  6 

6 

32 

11  6 

6  6 

21 

12  9 

6  9 

20  6 

13  6 

7  3 

21 

12  9 

7  3 

23  6 

14  3 

8  3 

15  3 

8  4 

5  0 

33  3 

20  4 

13  0 

28  7 

18  6 

34 

27  6 

16  3 

42 

26  6 

40 

25 

10  6 

34 

22 

9  0 

40 

24  6 

10  6 

42 

25  6 

10  6 

43 

25  6 

10  6 

42 

17  3 

10  6 

40 

25 

10  6 

34  8 

14  6 

9  3 

40 

14  0 

40 

9  7 

38 

9   10 

Speed. 


Knots. 
32.0 
20.48 

21.43 

36.58 

30.2 

27.1 

26.2 
26.0 

33.0 


36.0 

25.36 
18.02 

15.0 
15.0 
14.5 
18.0 
18.0 
21.73 

21.5 

20.7 

22.3 

2.S .  14 

23,53 

22.9 

21.75 


23.0 


24.0 
20.0 


Equiva- 
lent 
I.H.P. 

'A 

2,000 
S.-'SOO 

3 
3 

4,400 

3 

13,000 

4 

10,000 

4 

7,000 

4 

7,500 
3,600 

3 
3 

15,000 

3 

28,000 

4 

2,200 
3,800 

3 
3 

1,400 
1,800 
1,250 
4,000 
6,500 
8, .500 

3 
3 
2 
3 
3 
3 

6,000 

3 

6,500 

3 

7,000 

3 

8, .500 

3 

9,500 

3 

8,000 

3 

6,500 

3 

6,000 
9, .500 

3 
3 

12,000 
6.000 

3 
2 

Screws 
per 

Shaft. 

Dis- 
place- 
ment. 

Tons. 

Pro- 
peller 
Diam- 
eter. 

Lbs. 

3 

2,300 

210 

45 

1  6 

1  center. 

505  e 

1.50 

700 

4  9 

2  wing 

7.50  w 

4  4 

1 

750  c 
l,090w 

1.50 

900 

2 

1,180 

240 

390 

3  4 

3 

1,050 

240 

4.50 

2  9 

1 

890 

240 

440 

4  0 

2 

940 

2.50 

570 

3  3 

1 

1,200 

220 

225 

3  0 

1 

700 

220 

800 

6  0 

1 

600 

250 

1,.500 

7  0 

3 

1,200 

225 

145 

1 

550  c 
700  w 

180 

1 ,400- 

4  8 
4  0 

1 

900 

150 

900 

1 

1.50 

1,250 

1 

550 

160 

782 

1 

2,800 

1 

150 

3,100 

1 

480  c 
500  w 

150 

6  0 

5  7 

1 

480  c 
510  w 

150 

1,200 

1 

600 

150 

1,750 

5  0 

1 

670  0 
750  w 

150 

1.950 

5  0 

1 

5.30  c 
610  w 

200 

2,000 

6  2 

5  7 

1 

430 

160 

6  6 

1 

540 

150 

6  0 

1 

600 

150 

1,360 

5  3 

1 

600 
430 

490 

1 

160 
150 

1 

1.950 

1 

650 

2,000 

10 

11 

12 

13 
14 
15 
16 

17 
18 

19 

20 

21 

22 

23 

24 

25 

26 
27 

28 
29 


12. 
14. 
15. 
17. 
Samud 
IS. 
20. 
24. 
25. 
27. 
28. 
29. 


'^'afht  measurement. 

Thames  yacht  measurement. 

Thames  yacht  measurement.     Only  twin-screw  Parsons  installation. 

In  process  of  conversion  from  paddle  engines  to  turbines.      Vessel  built  in  1865  by 

i. 

.Screws  originally  arranged  as  in  King  Edward.      13  knots  astern  speed. 

Bow  riidder  fitted. 

Sister  ship  Invicta. 

See  "Engineering,"  .\ug.  IS,  1905. 

Three  building. 

Astern  speed  16.0  knots;  415  r.p.m. 

Curtis  turbines. 


298 


STEAM-TURBINES. 

TURBINE   STEAMERS— GENERAL 


Date. 


1904 

do. 

do. 

1905 

do. 

do. 

do. 
1904 

do. 

1905 
do. 
do. 

do. 

do. 

1903 

1904 
do. 
1905 
1903 


Vessel. 


Lhassa.  . . 
Loongana. 


Turbinia  II. 
Maheno.  ..  . 


Bingera. . 
Victorian. 


Carmania.  .  . 
Lusitania. .  . 
Mauretania. 
Ametiiyst.  . 


I.ubeck. 
Salem.  . 
Chester. 


Dreadnought . 


Orion  class. 
No.  243.  ..  . 


Libellule. 
Caroline. 


No.  293 

No.  294 

S.  125 

Revolution. 


Service. 


Persian  Gulf  to 
India.  Inter- 
mediate. 

Intercolonial 
Ser\nce,  Tasma- 
nia— Melbourne. 

Pleasure  Steamer 
Lake  Ontario. 

Inter-Colonial.  .  . 

Australian  Pas- 
senger. 

Atlantic    Inter- 
mediate Service 

Atlantic  Mail.  .  .. 
do 


3d-cla.ss  cruiser. 


do.  .  .  . 

Scout  Cruiser. 

do 


Battleship 

Armored  Cruisers, 
Experimental 
Torpedo  Boat. 

do 

do 


Torpedo  Boat 

do 

T.  B.  D 

Experimental 
S.  Y. 


Owner. 


British  India  S.  S.  Co. 


Union  S.  S.  Co.  of  New 
Zealand. 


Turbine  S.  S.  Co. 


Union  S.  S.  Co.  of  New 
Zealand. 


AUan  S.  S.  Co. 


Cunard  Co. 
do 


R.  N. 


German  Navy. 

U.  S.  N 

do 


R.  N. 


do 

French  Navy. 


do. 
do. 


do 

do 

German  Na\'y 

Curtis  Marine  Turbine 
Co. 


Builder. 


Denny  Bros. 


do. 


Hawthorn,  Leslie 

&  Co. 
Denny  Bros 

Workman  & 
Clarke. 

do 


John  Brown  &  Co. 

J.Brown&Co.,and 
Swan  &  Hunter. 

Armstrong,  Whit- 
worth  A- Co. 

Vulcan  Co 

Bath  Iron  Works. 

Fore  River  S.  & 
E.  Co. 

Portsmouth 
Dockyard. 


Soci^tii  des  F.  & 
C.  Mediterran^e. 


Yarrow. 


Normand. 

do.  .  .  . 

Schichau. 


.^0.  Sister  ships  lanka,  Lunka,  Lama. 
35.  Also  Virginian,  built  by  Stephen  &  Sons, 
tons.     Pai^.sengers  increased  60. 

37.  Two  building. 

38.  See  "Engineering,"  November  18,  1904. 
41.  Curtis  turbines. 

43.  Designs  still  under  consideration. 


Weight  saved  by  adopting  turbines,  400 


The  principal  reasons  for  the  present  tendency  to  adopt  the 
steam-turbine  in  place  of  the  reciprocating-engine  for  propelling 
ships  of  certain  types  are  the  following : 

1.  Decreased  cost  of  operation  as  regards  fuel,  labor,  oil, 
and  repairs. 

2.  Vibration  due  to  machinery  is  decreased. 

3.  Less  weight  of  machinery  and  coal  to  be  carried,  result- 
ing in  greater  speed. 

4.  Greater  simplicity  of  machinery  in  construction  and 
operation,  causing  less  liabiUty  to  accident  and  breakdown. 


THE  MARINE  STEAM-TURBINE. 


299 


DLMENSIONS    AND  D  XT  A.— {Continued). 


J 

Beam 

Q. 

"Sb 

p 

Speed. 

3  «    • 
o— " 

w 

Screws 

per 
Shaft. 

3 

Dis- 
place- 
ment. 

Pro- 
jpeller 
Diam- 
eter. 

d 
1" 

/     // 
275 

300 

260 
400 

44 

43 

33 
50 

/     n 

25  6 

25 

20  9 
33  6 

/     // 

12  6 
9  6 

Knots. 
18.0 

20.2 

19.0 
17.5 

6.000 
6,300 
3,500 

3 

3 

3 
3 
3 
3 

3 

4 

3 

4 
4 
2 

4 

4 
2 

Various 

650 
650 

Lbs. 
150 

150 

160 

Tons. 
2,170 

2,400 

1,100 

5  3 
4  1} 

30 
31 
32 

300 

?4 

540 

678 

785 

360 
341 

60 

72 
88 

40 

43  3 
46  8 
46  8 

42  6 
52 

27  6 

32 
33  6 

14  6 

16  6 
16  9 
16  9 

19.5 

21.0 
25.0 

21.75trial 

23.63des. 

22.0  des. 

24.0 

24.0 

21.0 

24.0 
21.0 

12,000 

21.000 
68,000 

9,800 
14,000 
10,000 
16,000 
16,000 

23.000 

28,000 
1,800 

275 

185 
165 

450  c 

490  w 

650 

500 

350 

300 

i.soo ' 

180 

195 
195 

250 

250 ' 
250 

250 

250 

13,000 
30,000 

as.uou 

3,000 

3,200 
3,750 
3,750 

18,000 

8  9 

14  0 
17  3 

6  6 

35 

36 
37 

38 

?9 

420 
420 

6  6 
9  3 

40 
41 

4'> 

43 

92 

Various 

do. 
do. 

Various 
4  6 

44 

45 

152  6 
125 

15  3 

14 
14 
23 
17 

8  4 

5  0 

26.4 

26.5 
26.0 
28.3 
18.0 

2,200 

2,200 
2.200 
6,000 
1,800 

3 
3 

Various 

575  R 
l.SOOT 

250 
250 

'256' 

140 

95 

95 

350 

46 

47 

125 

48 

200 

8  0 
7  0 

865 
650 

49 

140 

2 

50 

44.  Rateau  Turbines.     See  Trans.  I.  N.  A.,  1904. 

45.  Do. 

46.  Do. 

48.  Brequet  turbines.  49.   Astern  speed  16.7  knots.  50.  Curtis  turbines. 

Note. — Also  projected  two  vessels  for  Great  Central  Railway  Co.,  two  for  Allan 
Steamship  Co.,  two  for  the  Metropolitan  Steamship  Co.  (New  York  and  Bo.ston  Service), 
and  various  foreign  warships. 

5.  Smaller  and  more  deeply  iii:imersed  propellers,  decreas- 
ing the  tendency  of  the  machinery  to  race  in  rough  weather. 

6.  Lower  center  of  gravity  of  the  machinery  as  a  whole, 
and  increased  headroom  above  the  machinery. 

7.  According    to    recent    reports,    decreased    first    cost    of 
machinery. 

8.  The  adaptability  of  the  turbine  for  greater  power  devel- 
opment in  a  single  unit. 

The  application  of  the  turbine  to  dri\'ing  screw-propellers 
has  presented  a  number  of  new  problems  to  designers,  such  as 


300  STEAM-TURBINES. 

have  been  solved  and  reduced  to  more  or  less  nearly  standard 
practice  in  the  case  of  the  reciprocating-engine.  Among  these, 
the  greatest  importance  attaches  to  the  questions  of  reversibility 
of  turbines,  efficiency  of  propellers,  and  economy  at  slow  speeds. 

The  problem  of  reversing  has  been  met  by  the  use  of  special 
reversing  turbine  drums,  rotating  idly  in  the  exhaust-passage 
and  upon  the  shafts  of  the  low-pressure  turbines  when  the  ship 
is  going  ahead,  but  reversing  the  direction  of  rotation  of  the 
shafting  and  propellers  when  live  steam  is  made  to  act  upon 
the  blades  of  the  r  ever  sing-drums. 

The  determination  of  propeller  proportions  suitable  for  high 
speeds  of  rotation  is  still  the  subject  of  extensive  investigation, 
although  very  satisfactory  progress  has  already  been  made. 
The  problem  is  to  determine  the  proper  chameter,  amount  and 
distribution  of  blade  area,  and  the  proper  slip  and  pitch  ratios 
to  be  used  with  the  comparatively  high  rate  of  revolution  of 
the  steam-turbine. 

High  peripheral  velocity  of  turbine  blades  may  be  obtained 
either  by 

(a)  High  rate  of  revolution  and  small  diameter,  or 

(6)  Large  diameter  and  relatively  low  rate  of  revolution. 

For  satisfactory  efficiency  of  propulsion  with  screw  pro- 
pellers, certain  areas  of  propeller-blade  surface  are  required, 
according  to  the  thrust  demandetl,  and  it  has  been  found 
advisable  to  limit  the  number  of  propellers  to  one  upon  each 
shaft.  The  shafts  may  be  from  one  to  four  in  number.  There 
are  three  in  the  Carmania,  and  four  in  the  two  large  Cu- 
narders  at  present  under  construction.  The  requirement  for  a 
certain  amount  of  area  of  blade  surface  with  a  limited  number 
of  propellers  causes  a  limitation  of  the  speed  with  which  it  is 
safe,  or  otherwise  advisable,  to  rotate  the  shafts.  This  leads, 
in  vessels  of  large  displacement  and  high  power,  to  the  use 
of  large  diameters  of  the  rotating  members  within  the  turbine 
casings,  because  otherwise  the  speed  of  rotation  of  the  propellers 
would  often  be  such  as  to  cause  low  propulsive  efficiency.  The 
problem  presents  itself  to  the  designer  not  as  a  propeller  prob- 


THE  MARINE  STEAM-TURBINE  301 

lem  alone,  capable  of  solution  for  any  rate  of  revolution  that 
may  be  adopted  for  the  turbines,  but  as  a  question  of  the 
proper  interrelation  of  steam  velocities,  diameter  and  rate  of 
rotation  of  turbines,  and  size  and  proportions  of  the  screw- 
propellers. 

This  suggests  the  chief  difTerence  in  point  of  design  between 
turbines  for  driving  alternating-current  machinery  and  these 
for  rotating  the  shafts  of  screw-propellers.  The  stationary  tur- 
bine may  be  operated  at  a  high  rate  of  revolution,  with  increas- 
ing efficiency  and  decreased  size  and  weight  of  part  accom- 
panying the  increase  in  speed.  The  marine  turbine,  especially 
for  large  powers,  is  called  upon  to  turn  the  propellers  at  the 
relatively  low  rate  of  revolution  giving  satisfactory  propulsive 
efficiency.  Since  both  types  require  certain  peripheral  veloci- 
ties in  order  to  utiUze  the  energy  of  the  steam  efficiently,  the 
result  is  relatively  high  speed  of  rotation  for  the  stationary 
turbine,  with  as  small  diameters  as  possible  so  as  to  reduce 
centrifugal  forces;  and  large  diameters  of  the  marine  turbine, 
with  correspondingly  low  rates  of  revolution,  for  obtaining 
efficiency  of  screw-propellers. 

Further  difference  in  the  arrangement  of  the  two  types  is 
occasioned  by  the  demand  for  close  regulation  of  speed  in  the 
stationary  turbine,  and  for  reversibility  in  the  marine  turbine. 
The  latter  must  be  capable  of  sudden  reversal  of  direction  of 
rotation,  and  of  ready  handling  at  all  speeds  for  maneuvering 
the  vessel. 

In  general,  with  the  larger  turbine-boats  that  iiave  been 
built,  the  economy  has  been  somewhat  lower  at  speeds  below 
14  knots  than  in  boats  driven  by  reciprocating-engines,  but 
above  this  speed  the  turbine-boats  have  exceeded  in  economy, 
and  the  rate  of  increase  with  increased  speed  has  been  very 
marked.  This  is  shown  by  the  economy  curves  on  pages  302 
and  303  representing  trials  of  torpedo-boat  destroyers  and 
cruisers.* 

*  The  curves  and  the  table  on  pages  296-299  are  from  a  paper  by  Mr.  E. 
M.  Speakman,  Trans.  Am  See.  Naval  Architects  and  Marine  Engineers,  Vol. 
13,  1905:  "  Marine  Turbine  Development  and  Design." 


302 


STEAM-TURBINES. 


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Speed 

Fig.  121. — Economy  curves  of  crui.sers. 


304 


STEAM-TURBINES. 


The  following  table  *  shows  the  steam  consumption  of  the 
four  Midland  Railway  steamers  recently  built  and  tested.  The 
Antrim  and  Donegal  are  equipped  with  reciprocating-engines, 
each  vessel  having  two  sets  of  four-cylinder  triple-expansion 
engines,  each  driving  a  three-bladed  propeller.  The  cylinders 
are  23  inches,  36  inches,  and  two  of  42  inches  diameter,  with 
30-inch  stroke  of  pistons. 


Gallons  of  Water  Consumed  per  Hour. 

Speed  in  Knots 
f>er  Hour. 

Reciprocating, 

Antrim  and 

Donegal. 

Turbine. 

Londonderry. 

Manxman. 

14 
17 
20 
22 
23 

4,500 
6,700 
9,700 

4,500 

6,100 

8,900 

13,600 

4,500 

5,800 

8,300 

12,500 

17,300 

The  arrangement  of  the  turbines  in  the  Londonderry  and 
Manxman  differs  only  in  detail,  but  the  turbines  in  the 
Manxman  are  larger,  as  they  were  designed  for  25  per  cent 
more  power  than  the  Londonderry.  There  are  three  tur- 
bines in  each  vessel,  one  high-pressure  and  two  low-pressure. 
The  reversing-turbines  work  upon  the  low-pressure  shafts,  and 
rotate  in  vacuum  when  not  in  use.  Each  of  the  three  turbines 
drives  a  three-bladed  propeller. 

The  dimensions  of  the  four  vessels  are  alike,  with  the  ex- 
ception that  the  Manxman  is  of  slightly  greater  beam  than 
the  others.  The  length  on  the  water-line  is  330  ft.;  moulded 
breadth,  42  ft.;t  moulded  depth,  25  ft.  6  in. 

The  amount  of  water  consumed  was  measured  during  the 
progressive  trials  by  counting  the  strokes  of  the  feed-pumps. 

Mr.  Parsons  has  made  the  following  J  prediction  as  to  the 
future  of  the  steam-turbine  for  marine  use:  "...  With  the 
evidence  at  present  before  us,  I  think  we  are  safe  in  predicting 

*  London  Engineering,  August  4,  1905. 

t  Excepting  the  Manxman,  of  43  feet  beam. 

J  Trans.  Inst.  Marine  Eng.,  London,  1904-5. 


Fig.  122. — Cross-section  througli  inuchiaery  space,  steanship  Carinania, 

305 


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atiojj  asd  m\iais  JO  's^T  l^J^Oi 


THE  MARINE  STEAM-TURBINE. 


307 


Upper  Dcik 


^iG.  124.— Arrangement  of  machinery  in  S.S.  Carmania. 
(From  "Engineering,"  London,  Dec.  1,  1905.) 


308  STEAM-TURBINES. 

that  it  will  soon  supersede  entirely  the  reciprocating-engine  in 
vessels  of  16  knots  sea-speed  and  upwards,  and  of  over  5000 
I.H.P.,  and  probably  also  inchuling  vessels  of  speed  down  to 
13  knots,  of  20,000  tons  and  upwards,  and  possibly  still  slower 
vessels  in  course  of  time.  At  present  it  may,  I  think,  be  said 
that  the  above  most  suitable  field  comprises  about  one  fifth  of 
the  total  steam  tonnage  of  the  world;  but  it  must  be  remem- 
bered that  the  speed  of  ships  tends  to  increase,  and  the  turbine 
to  improve,  and  so  the  class  of  ships  suitable  for  the  turbine 
will  increase." 

The  growth  of  the  application  of  the  Parsons  turbine  to  steam- 
ship propulsion  is  represented  in  Fig.  125.  At  the  left  is  shown 
the  progress  in  application  to  war  vessels,  advancing  from  the 
experimental  "Turbinia  "  to  the  battleship  "Dreadnaught,"  and 
at  the  right  the  progress  in  application  to  merchant  and  passen- 
ger vessels,  culminating  in  the  production  of  the  largest  vessels 
afloat,  the  Cunard  steamers  "Lusitania  "  and  "Mauretania," 
785  feet  long  and  of  25  knots  speed.  These  remarkable  vessels 
and  their  turbines  are  shown  in  Figs.  126,  127  and  128. 

Fig.  129  shows  a  number  of  arragements  of  Parsons  turbines 
suitable  for  various  classes  of  vessels.  It  is  to  be  noted  that 
several  of  these  arrangements  show  four  propeller  shafts.  In 
general  the  reciuirement  for  great  power  in  a  ship  calls  for  its 
distribution  between  several  units  as  has  been  the  case  with  the 
"Lusitania  "  and  "Mauretania."  It  is  possible  and  customary 
in  certain  classes  of  work  to  build  single  turbines  to  develop 
considerably  more  power  than  it  is  practicable  to  develop  in  a 
single  reciprocating  engine.  But  for  very  high  powers  the  size 
of  shafting  and  other  parts  becomes  necessarily  so  great  that  it 
is  often  found  advisable  to  distribute  the  power  between  several 
units,  especially  when  the  speed  of  rotation  is  low. 

Figs.  I'M)  to  134  inclusive  show  the  steamer  "Creole  "  and  the 
turbines  for  propulsion.  The  ship  was  built  by  the  Fore  River 
Shipbuilding  Company  for  the  Southern  Pacific  Raihvav  Com- 
pany, is  440  feet  long,  and  has  a  speed  of  about  17  knots. 
The  small  turbi-ne  shown  in  the  foreground  of  Fig.  131  was  de- 


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Fig.  127. — Stern  View  ISliowing  Rudder  and  Two  of  the  Four  Propellers,  Str. 
Mauretania,Cunard  Line.  Sister  Ship  to  Lusitania.  (From  *'  Engineering," 
London.)  311 


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partments, 2  Cruising  'i'urbines. 


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Turbines.     1  Compartment. 


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partments, 2  Cruising  Turbines. 


Merchant  Ship,  4  Shafts,  all  Reverein."^.     2 
Compartments. 


Torpedo  Boat,  3  Shafts,  1  Reversing,  1 
Crusing  Turbice.    1  Compaitment 


Merchant  Ship,  4  Shafts,  all  Reversing. 
2  Compartmenta. 


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partments, 1  Cruising  Turbine. 


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partments, 2  Cruising  'lurbines. 


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partments, 2  Cruising  'I'urbines. 


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5  Comparlmeuts. 


Warship,  4  Sliafts,  all  Reversing.    2 
Compartments,  2  Cruising  lurbines. 


Fig.  129. Possible  Armngement  of  Parsons  Turbines 

in  Vessels  of  Various  Classes.  From  a  Paper  by  Mr. 
Chas.  A.  Parsons.  Reproduced  from  Reprint  in 
"Engineering,"  London,  July,  1907. 


To  face  page  312. 


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314  STEAM-TURBINES. 

signed  for  a  battleship  tender,  to  develop  250  H.P.  at  1200  r.p.m., 
while  each  of  the  main  turbines  for  the  "Creole  "  develops  4000 
H.P.  at  about  235  r.p.m. 


Fig.  131. — One  of  the  two-4000  Horse-power  Curtis  Turbines  of  the  Steamer 
"  Creole,"  and  a  250  Horse-power  Curtis  Turbine  for  Battleship  Tender. 

The  first  large  turl:)ine  steamers  to  be  i)ut  on  the  transatlantic 
service  were  the  Allan  line  boats,  "Victorian"  and  "Virginian," 
of  about  18  knots  speed.  The  arrangements  of  the  turbines, 
condensers,  shafting,  and  of  the  steam-piping,  are  shown  in  Figs. 
135  and  136.  One  of  the  condensers  of  the  "Victorian,"  with  Mr. 
Parsons'  Vacuum  Augmenter,  and  with  the  air-pumps,  is  shown 
in  Fig.  137. 

With  the  devolopmcnt  of  the  turbine  has  come  the  necessity 
for  measuirng  the  power  delivered  to  the  shaft.  Two  methods 
are  illustrated  here,  the  first,  that  involving  the  application  of  a 


FiQ.  134.— Curtis  Murine  Turbine  as  I'itU-d  on  Steamer  "Creole." 

Tojace  page  315. 


Fig.  132. — Showing  Nozzles  of  one  of  the  Lowest  Pressure   Stages,  Curtis 
Turbines  for  Steamer  "  Creole."    The  Turbines  have  Seven  Stages  Each. 


Fig.  133. — One  of  the  Rotating  Wheels,  Curtis  Turbines  for  S  enmer 

"  Creole."  31.5 


idsaapao^  '/j«}D9mSnv 


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316 


Fig.  139. 

Diagrams  obtained  witli  Foettinger  Torsion  Indicatnr  from  Rp,ip,ocalinp  Engines  and  showing  tlie  Mechnnical 
Efficiency  or  Relation  between  the  DcUveredand  hidic;ilcd  Horse-power  of  the  Engine.';. 

To  face  pfigp  'il? 


Fio.  140— Foettinger  Torsion-meter  applied  to  Oerman  Truisors.     ReproJucoil  from  Paricr  by  Mr  E.  M.  Speakmaii,  Inst,  of  I'^sinrers  and  Shiplmildens  oC  Sciitlnnil^  \  o^.^ 


Fic  142      Fiagviimmatic  Ucf  resent ation  of  Denny  and  .Ii 


Twin  Screw  Steanjer 
sbowinp  Indicated 
H.  P.  and  Shaft  H.  P. 

/ 

^ 

Sljaft  H.  P. 

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,1.  H.  P. 

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Twin  Screw  Steamer 
showing  Indicated 
H.  P.  and  Shaft  H.  P. 


. 

Shaft  H.  P.  X 

Ij 

w 

I.  i.p. 

f- 

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A 

Twin  Screw  Steamer 

HigllebtSpeed  2U.7  Knuts. 

Turbine  Steamer 

Highest  Speed  21 .37  Knots. 


£  = 

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Fig.  1-13.— Diagram  showing  Relation  between  Delivered  and  Indicated  Horse-power. 

HeproJuciid  from  "Kiigineeiing,"  London. 

To  face  page  317. 


To  Backing  Tmbine 


i^ 


Backing 
Tmbine 


L.P.  Turbine 


H.P.  Turbine 


Foward 


i3 


'J  Vertical  Pipe 


farnti 


S^^  Boilers 
'J  Vfcitical  Pipe 


Backing 
Turbine 


L.P.  Turbine 


^ 


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5  ■^ 


^ 


Fig.  135. — Arrangement  of  Steam-piping,  Steamer  "  Victorian.' 


Exhaust  to  Condenser 


Fig.  137. — Condensers  and  Air-pumps,  Steamer  Victorian,  Allan  Line. 

317 


w 


sf  c 


fe 


THE  MARINE  STEAM-TURBINE.  319 

water-brake  to  the  shaft;  and  the  seeond,  that  in  which  the  arc 
of  torsion  of  a  certain  length  of  shafting  is  measured  while  power 
is  being  transmitted  by  the  shaft.  All  shafts  twist  to  some  ex- 
tent under  the  influence  of  torque,  and  for  stresses  below  the 
elastic  limit  of  the  material  the  arc  of  torsion  is  proportional  to 
the  torque.  The  first  successful  torsion-meter  for  turbine  use 
was  developed  in  Germany  by  Dr.  Foettinger,  of  Stettin,  upon 
the  basis  of  the  extensive  exj^eriments  made  by  Hermann 
Frahm  of  Hamburg  to  ascertain  the  extent  of  the  torsional 
vibration  of  the  shafting  of  reciprocating  engines.  The  Foet- 
tinger torsion-meter  is  shown  in  Fig.  138,  and  diagrams  ob- 
tained by  its  use  in  Figs.  139, 140, 141,  inclusive.  The  Dermy- 
Johnson  torsion-meter  was  developed  by  Messrs.  Denny  Brothers 
of  Dumbarton,  Scotland.  This  meter  is  represented  in  Fig.  142, 
and  results  obtained  are  shown  in  Fig.  143.  Torsion-meters 
have  yielded  most  valuable  information  as  to  the  mechanical 
efficiency  of  reciprocating  marine  engines,  and  have  thereby 
contributed  materially  to  the  available  information  concerning 
ship  propulsion. 

Water-brakes  are  not  convenient  for  application  aboard  ship, 
but  are  extensively  used  in  shop  tests  of  turbines.  Numerous 
forms  of  water-brake  have  been  devised,  but  in  all  the  power 
developed  by  the  turbine  is  expended  in  setting  water  in  motion 
by  means  of  rotating  metal  discs  or  wheels.  The  torque  is 
measured  by  weighing  the  pull  on  a  brake-arm  attached  to  the 
casing  in  which  the  rotating  member  is  enclosed.  The  casing 
tends  to  rotate  because  of  the  action  of  the  water,  which  is  set 
in  motion  by  the  rotating  discs  of  wheels.  The  water  is  of 
course  heated  by  the  frictional  resistance  opposed  to  its  motion. 
Figs.  144  and  145  show  one  form  of  water-brake  which  is  suc- 
cessfully used  in  turbine  tests. 


APPENDIX. 


Cost  of  Steam-turbines. — The  curves  on  page  321  represent 
the  selUng  price  of  turbines  and  generators  combined,  as  quoted 
by  various  builders  in  1905.  Averages  of  quotations  from  the 
different  firms  were  taken  for  plotting  the  curves.  The  upper 
right-hand  section  of  the  page  gives  curves  of  selling  prices  for 
comparatively  small  machines,  connected  to  direct-current 
generators  of  f:om  10  K.W.  to  300  K.W.  capacity.  The  lower 
curves  are  'or  large  machines — from  300  K.W.  to  7500  K.W. 
— ^with  alternating-current  generators  The  curves  are  given 
to  show  the  manner  in  which  the  seUing  price  varies  -^dth  the 
conditions  of  operation,  but  the  values  represented  do  not 
correspond  exactly  with  the  quotations  of  any  one  company. 

320 


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STEAM-TURBINES. 


321 


Selling  Price, -Dollars,  10  K.W.  to  300  K.W. 
100        90         60         70         CO        50         40         30         80         10 


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Selling  Price,  Dollars. 
For  MacUiues  from  300  K.W.  t.o  7600  K.W.  [^Current"^ 


50 


EXAMPLES. 

SET  NO.  1. 
Text  Reference,  Pages  6-20. 

1.  One  quarter  pound  of  steam  flows  per  second  from  a  vessel  fitted 
with  an  orifice  having  a  least  cross-sectional  area  of  .025  sq.  in  Let 
the  specific  volume  of  the  steam  while  in  the  orifice  be  2.0  cu.  ft.  per 
pound. 

(a)  Compute  velocity  of  flow. 

(6)  Compute  the  reaction  accompanying  the  flow. 

2.  If  the  steam  should  act  upon  the  buckets  of  a  turbine-wheel,  leav- 
ing same  at  a  velocity  of  1000  ft.  per  sec, 

(a)  What  horse-power  will  be  given  up  to  the  wheel,  assum- 
ing there  are  no  frictional  losses? 

(h)  Compute  the  efficiency  of  wheel  from  the  above  con- 
siderations. 

(c)  If  the  exhaust,  at  1000  ft.  per  sec,  should  act  upon  the 
buckets  o£  another  wheel,  leaving  same  at  300  ft.  per  sec,  how 
much  power  would  the  two  wheels  together  deliver,  disregarding 
losses? 

(d)  What  would  be  the  efficiency  of  the  system? 

3.  A  vane  such  as  that  shown  in  Fig.  9,  page  18,  moves  with  a  velocity 
of  1200  ft.  per  sec,  and  is  acted  upon  by  a  jet  of  steam  having  an  initial 
velocity  F,  of  3400  ft.  per  sec  The  angle  a  =24  degrees  and  /?  =  30 
degrees. 

(a)  If  one  quarter  pound  steam  per  sec.  acts  upon  the  vane, 
compute  the  impulse  of  the  jet  upon  the  vane. 

(b)  Find  the  proper  value  of  the  angle  of  the  entering  side 
of  the  vane,  so  that  the  steam  may  enter  without  loss  from  impact. 

SET  NO.  2. 
Text  Reference,  Chapter  III. 
A  pound  of  water  at  520  degrees  F.  absolute  is  heated  until  its 
temperature  becomes  790  degrees  absolute. 

(a)  Assuming  its  mean  specific  heat  to  be  1.006  for  the  temperature 
range  in  question,  how  much  heat  is  required  to  accompUsh  the  rise  in 
temperature? 

(6)  What  increase  in  entropy  has  accompanied  the  addition  of  heat? 

322 


EXAMPLES.  323 

(c)  If  further  heat  be  added  until  the  entropy  of  the  resulting  mix- 
ture of  steam  and  water  is  1.55,  as  shown  on  the  chart  at  the  back  of 
the  book,  what  will  be  the  percentages  of  steam  and  of  water  present? 

(d)  If  the  mixture  should  expand  adiabatically  in  a  nozzle  to  a 
pressure  of  10  lbs.  absolute,  what  would  be  the  resulting  velocity  of 
flow  from  the  nozzle  under  ideal  conditions? 

(e)  What  would  be  the  quality  of  the  exhaust  from  the  nozzle? 

(/)  If  sufficient  heat  had  been  added  in  (c)  to  evaporate  the  pound 
of  water  into  dry  and  saturated  steam,  how  much  tJiorc  heat  would 
be  required  to  superheat  the  dry  steam  to  a  temperature  100  degrees 
above  the  saturation-paint,  assuming  the  mean  specific  heat  of  super- 
heated steam  to  be  .58? 

ig)  To  what  temperature  would  the  superheated  steam  have  to  fall, 
adiabatically,  in  order  to  become  just  dry  and  saturated? 

{h)  If  the  expansion  indicated  in  (g),  of  the  superheated  steam, 
occurred  in  a  suitable  nozzle,  so  that  the  energy  liberated  all  appeared 
as  kinetic  energy  of  flow,  compute  the  velocity  of  the  issuing  steam-jet. 

SET  Xo.  .3. 
Text  Reference,  Chapters  IV  and  Y. 

Design  a  nozzle  for  carrjang  out  the  expansion  of  .25  pound  steam 
per  second,  under  the  following  conditions: 

Let  the  initial  pressure  be  165  pounds  absolute  =/>■.. 

"     "    final  "        "       2       "  "       =;v 

"  "  loss  of  energy  in  the  passageway  be  that  corresponding  to 
y  =  .U. 

Let  the  steam  before  entering  the  nozzle  be  98.5  per  cent  dry. 

Find  the  proper  cross-sectional  areas  for  the  nozzle  at  points  where 
the  pressure  is  95  pds.,  75  pds.,  60  pds.,  45  pds,  30  pds.,  15  pds.,  and  2 
pds.,  absolute,  per  sq.  in. 

Let  the  interior  of  the  nozzle  be  conical  in  form,  4"  long. 

Make  a  sketch  of  the  nozzle  to  scale,  and  plot  curves  of  pressure  fall 
and  velocity  similar  to  those  on  page  149. 

Typical  calculations  are  given  on  page  85. 

SET  XO.  4. 
Text  Reference,  Pages  151-1.3S. 
Let  steam  expand  in  the  nozzles  of  a  simple  impulf-e  turbine  (de 
Laval  type)  from  120  pounds  absolute  to  a  vacuum  of  27"  mercury. 
Let  the  nozzle  make  an  angle  a  =28°  with  the  plane  of  rotation  of  the 
buckets.  Let  the  peripheral  velocity  of  the  buckets  be  1300  feet  per 
second.     Find  steam  velocity  from  Plate  XL 


324  EXAMPLES. 

(a)  Draw  velocity  diagrams,  allowing  for  no  losses,  and  compute 
the  energy  given  up  to  the  buckets,  per  pound  of  steam,  and  compute  the 
steam  consumption  of  the  deal  turbine,  and  the  efficiency.  Make  a  sketch 
of  the  buckets  on  the  velocity  diagram. 

(b)  Let  the  loss  of  energy  in  the  nozzles  correspond  to  y=.lo,  and  in 
the  buckets  let  y'  =  A3. 

(1)  Draw  velocity  diagrams,  and  sketch  in  the  bucket  outline. 
Note  the  change  in  bucket  angles,  made  necessary  by  the  losses. 

(2)  Compute  the  work  done  per  pound  of  steam,  and  the  steam 
consumption  per  horse-power  hour. 

(3)  Compute  the  efficiency  of  the  turbine. 

(4)  If  the  revolutions  of  the  wheel  are  14,000  per  mipute,  find 
diameter  of  mean  bucket  circle. 

(o)  If  seven  nozzles  are  used  at  ma  imum  load  of  75  K.W. , 
find  least  diameter  of  the  nozzles,  by  means  of  the  curve  of  dis- 
charge on  Plate  XL 


SET.    XO.   5. 

Text  Referen'ce,  Pages  158-175. 

(a)  Draw  velocity  diagrams  for  an  impulse  turbine  of  two  stages  and  three 
rows  of  moving  blades  in  each  stage,  according  to  the  following  data. 

Let  the  turbine  be  required  to  develop  1000  K.W.  at  full  load  and  1400 
K.W.  at  maximum  overload.  Efficiency  of  generator =94%.  Let  the  initial 
pressure  at  inlet  be  145  pds.  gauge,  and  let  the  steam  expand  to  15  pds.  abs. 
in  the  first  nozzles,  and  in  the  second  nozzles  from  15  pds.  abs.  to  a  vacuum 
of  28^  in.  mercury.  Let  the  angle  of  nozzles  with  plane  of  rotation  of  buckets 
be  22°.  Let  peripheral  velocity  of  buckets  be  420  ft.  per  sec.  Assume  that 
the  frictional  losses  are  represented  by  the  values  of  y  given  on  pages  164  and 
168  respectively,  and  let  the  work  lost  because  of  journal  friction,  windage, 
and  leakage  be  259c  of  t^^  work  done  by  the  steam.  Draw^  diagrams  as  on 
Plate  XII,  and  compute  steam  consumption  per  H.P.  as  on  pages  166  and 
169,  arranging  for  the  maximum  overload  requirement. 

Let  R.P.M.  be  1800.  Compute  height  of  second  stage  nozzles  follow- 
ing the  method  given  on  pages  170,  etc.,  and  according  to  the  following 
data:  Let  thickness  of  nozzle  walls  be  0.075  m.  and  let  pitch  of  nozzles  be 
1.5  in.  Let  the  nozzles  subtend  an  angle  at  center  of  turbine  shaft,  of  J  =  130 
deg.  If  height  of  first  row  of  buckets  is  2^%  greater  than  that  of  the  nozzles, 
and  if  height  ratio  for  second  stage  is  1.6,  compute  height  of  last  buckets  in 
the  stage. 

ib)  A  turbine  takes  steam  at  175  pds.  abs.  and  125  deg.  F.  superheat,  and 
expands  adiabatically  to  a  vacuum  of  27.8  in.  mercury.  Find  available 
energy  from  the  Mollier  Heat  Diagram  opposite  p.  320.  How  much  steam 
would  a  perfect  engine  use  under  these  conditions  ?    If  a  test  of  an  actual 


EXAMPLES.  325 

turbine  shows  a  steam  consumption  of  12  pds.  per  horse-power  hour,  what  is 
the  efficiency  of  the  engine  ?     (See  pages  175-6). 

Let  the  horse-power  be  3000  and  let  the  R.P.M.=900.  Let  the  bucket 
speed  be  350  ft.  per  sec.     Compute  diam.  of  turbine. 

Let  the  turbine  have  six  stages  and  let  the  energy  distribution  aimed  at 
be,  First  stage,  0.25  E.  and  each  succeeding  stage  0.15  E. 

Let  the  first  stage  efficiency  be  0.45  and  for  each  remaining  stage  let  effi- 
ciency  =  0.50. 

Find  the  area  required  through  nozzles  of  last  stage,  in  order  to  provide  for 
3000  H.P.  Assume  the  nozzle  particulars  to  be  the  same  as  stated  at  bottom 
of  page  187,  and  compute  necessary  height  of  nozzles  for  the  last  stage  of  the 
turbine. 

Note  that  the  diagram  on  the  back  cover  of  the  book  sJiow.s  an 
expansion  curve  representing  the  calculated  expansion  of  steam,  as  given  on 
page  18G. 

The  heat  contents  of  steam  may  be  taken  from  either  the  Heat  Diagram 
opposite  page  320  or  from  the  one  on  the  back  cover,  but  the  former  is  pre- 
ferable, especially  as  it  is  well  to  become  familiar  with  the  Mnllier  Diagram  as 
used  in  practice. 

SET    XO.   6. 

Text    Refere.xcs,    Pages    189-195. 

Turbine  of  the  Parsons  Ty{3e,  2500  B.H.P.,  1800  R.P..M. 

Initial  steam  pressure,  165  pds.  abs. 

Initial  superheat,  100  deg.  F. 

Vacuum  28^  inches  mercury. 

Ratio  peripheral  to  steam  velocity  =  0.55. 

Turbine  to  have  3  cylinders,  and  let  the  mean  peripheral  velocities  in 
the  cylinders  be  respectively  140,  220  and  325  tt.  per  sec. 

Let  the  heat  absorbed  by  the  various  cylinders  be,  H.P.  2S<^  LP.  32%, 
and  L.P.  40%. 

Assume  adiabatic  expansion  and  calculate  nutnljcr  of  rows  and  mean 
diameters  of  the  cylinders. 

Let  the  annular  sjxace  occupied  by  blades  have  2.6  times  the  cress  sec- 
tional area  required  for  steam  flow. 

Let  the  steam  consumption  at  full  load  be  13  j)ounds  per  B  H.P.  hour. 
Assume  that  the  steam  pres.sure  after  passing  the  throttle  valve  is  14  i  pds. 
abs.  and  has  dropped  to  this  along  a  constant  heat  curve.  Find  sj)ecific 
volume  at  entrance  to  the  first  cylinder.  Compute  blade  lengths  at  entrance 
to  and  at  exit  from  each  of  the  cylinders,  as  on  j>ages  193-4.  Let  the 
steam  velocity  at  the  last  rows  of  the  L.P.  cylinder  be  1000  ft.  per  sec. 
instead  of  remaining  constant  during  passage  through  that  cylinder. 

Tabulate  results  as  on  page  195. 


TECHNICAL  PAPERS  AND  REPORTS  RELATING  TO  STEAM- 

TURBLXES. 

The  best  economy  of  the  piston  steam-engine  at  the  advent  of  the 
steam-turbine.     Journal  of  American  Soc.  Naval  Engineers,  Feb.  1905. 

The  Rateau  Steam-turbine,  and  its  applications.  ^L  J.  Rev.  (Trans- 
lation.)    Journ.  Am.  Soc.  N.  E.,  Nov.  190.5. 

Steam-turbines  with  special  reference  to  their  adaptability  to  the 
propulsion  of  ships.     E.  N.  Jan.son,  Journ.  Am.  Soc.  N.  E.,  Feb.  1904. 

The  determination  of  the  i:)rincipal  dimensions  of  the  steam-turbme, 
with  special  reference  to  marine  work.  E.  M.  Speakman,  .Journ.  Am. 
Soc.  N.  E.,  Feb.  1906. 

Report  concerning  the  design,  installation,  and  operation  of  the 
turbine  engines  of  the  S.  S.  Revolution,  Jour.  Am.  Soc.  N.  E.,  Nov.  1903. 

Report  of  Board  to  observe  and  report  concerning  the  efficiency  of 
turbine  engines.     Jour.  Am.  Soc.  N.  E.,  Nov.  1903. 

Reports  on  turbine  installations  on  steam  yachts  Lorena  and  Taran- 
tula, and  Str.  Turbinia.  Canaga-Janson,  Jour.  Am.  Soc.  N.  E.,  Nov. 
1904. 

Comparative  trials  of  turbine  cruiser  Amethyst,  and  the  reciprocating 
engine  cruisers  Topaz,  Emerald,  and  Diamond.  Engnieermg,  London 
Nov.  18  and  25,  1904. 

Some  theoretical  and  practical  considerations  in  steam-turbine 
work.     Francis  Hodgkinson,  A.S.M.E.,  No.  .031,  1904. 

The    Steam-turbine    in  modern    engineering.      W.    L.    II.    Kinmet 
A.S.M.E.,  No.  104fi,  1904. 

The  DeLaval  Steam-turbine.     E.  S.  Lea,  A.S.M.E.,  No.  1047,  1904. 

Report  of  the  Committee  for  Investigation  of  the  Steam-turbine. 
National  Electric  Light  Assoc,  1905.     136  Liberty  St.,  N.  Y 

The  Steam-turbine.  Chas.  A.  Parsons,  Inst.  Elec.  Engineers.  London, 
May  1904. 

The  efficiency  of  surface-:Condensers.  R.  L.  Weighton,  Inst.  Naval 
Architects,  London,  April  5,  190(). 

Experiments  on  surface-condensation.  James  A.  Smith.  Engineer- 
ing, London,  Mar.  23.  1906. 

The  effect  of  admission  pressure  upon  the  economy  of  steam  turliujes 
T.  Stevens  and  H.  M.  Hobart,  Engineering,  London,  .Mar.  2  and  9,  1906. 

327 


INDEX. 


A. 

Acceleration,  1. 

Adiabatic,  expansion,  31;   process,  41. 

Air-jet,  impulse  of,  133. 

Allan  Line  Steamers  "Victorian"  and  "Virginian,"  317. 

Analysis  on  basis  of  heat  expenditure,  230. 

Angles  of  buckets,  126. 

Apparatus — Wilson's,   140;    Sibley  College,  141. 

Arrangements  of  marine  steam  turbines,  312. 

Auxiliaries,  290. 

B. 

Back-pressure,  effect  of,  143,  145. 

Blade,  speed  of,  21;  length  of,  223;  Parsons,  266. 

Buckets,  angles,  126;  additional  sets  of,  130;  and  nozzles,  clearance  be- 
tween, 129;  clearance  between  rows  of,  132;  Cutting  over  edges, 
135;  Curtis  turbine,  163,  278,  experimental  work,  93,  123;  length 
of,  187;  spacing,  126;   surface,  effect  of  roughness,  135,  137. 


C. 

Calorimeter  for  use  in  heat  analysis,  235,  242. 

Calorimeter,  sampling  tube  for,  242. 

Classification  of  steam  turbines,  xiii. 

Carnot  cycle,  42;  efficiency  of,  43. 

Clearance  between  nozzles  and  buckets,  129,  288. 

rows  of  buckets,   132,   288.    ' 
Condenser,   size   of,    290. 
Condensers,  counter-current,  294. 
Cost  of  turbines,  Appendix,  320. 
"Creole,"  Steamer,  313,  315. 
Cunard  Steamer  "Lusitania,"  310,  312. 
Cunard   Steamer   "Mauretania,"   310,  312. 

329 


330  INDEX. 

Curtis  turbine,  buckets,  163;   discussion,  264;   four-stage,  275;   tests  of. 

282. 
Curtis  turbine,  calculation  of  dimensions,  182. 
Curtis  turbine  nozzles,  design  of,  171,  175. 
Curtis  turbine  Steamer  "Creole,"  313,  315. 
Cutting  over  edges  of  buckets,  135. 
Curves,  characteristic,  209,  211,  219,  224. 


D. 

De  Laval  nozzles,  114,  248;    turbine,  general  description,  246;    tests  of, 

250,  252. 
Denny-Johnson,  torsion  meters,   319. 
Design  of  Curtis  turbine  nozzles,  171-175. 
Design  of  impulse  turbines,  176. 
Design  of  turbines,  geneial  remarks,  292. 
Diagrams,  impulse-turbine,  155. 

Diameter  of  wheels,  170;  of  rotor,  217,  222;   of  spindle,  217,  222. 
Dimensions  of  nozzles,  85,  122. 
Divergent  nozzle,  69. 
Dynamic  pressure,  6. 

E. 

Economy  of  turbines,  285;   of  marine  turbines,  303,  304. 

Efficiencies,   comparison  of,   225;    variations   of,   227,   229;    efficiency   of 

turbine,  21,  23. 
Efficiency,  experimental  determination  of,   176. 
Efficiency  of  turbines,  175. 
Energy,  intrinsic,  28. 

Entropy,  47;   calculation  of,  45;    diagram,  39;   units  of,  52. 
Equation,  Napier's,  99;   Zeuner's,  28,  31. 
Expansion,  adiabatic,  31;   isothermal,  30;   of  steam.  30,  55. 
Experimental  work,  93;   Sibley  College,  123. 


Fliegner,  38. 
Flow,  of  gas,  33. 

"     of  steam.  27,  35,  62;   experimental  work,  93. 

"     rate  of,  140;  resistances  to,  77;  velocity  of,  72;  weight  of,  64,  65,  71. 
Foettinger  torsion  meters,  319. 
Force,  uniform.  1;   unit  of,  3. 
Frictional  effect,  curve  of,  202,  219. 

"  losses,  determination  of,  88;   variation  of,  218. 

*'  resistances,  77,  149. 


INDEX.  331 


Friction,  skin,  139;   work  of,  81. 
Froude,  William,  38. 


G. 


Gas,  flow  of,  33. 

Graphical  representation  of  heat  transformations,  39. 

Gutermuth,  Professor,  38,  95. 

H. 

Hall.  Thomas,  123. 

Heat   analysis,   230. 

Heat  analysis,  calorimeter  for,   235-242. 

Heat,  curves  of  constant,  53;  total,  curves  of  constant,  51;  diagram,  39; 

diagram,  examples  in   use  of,   54;    specific,   44;    transformations, 

graphical  representations  of,  39. 
Heat  diagram,  MoUier,  53-60. 


Impact,  19. 

Impulse,  19,  26. 

Impulse  of  a  jet,  5;  of  air-jet,  133. 

Impulse  turbines,  design,  176. 

Impulse-turbine,  general,  xi;   discussion  and  design  of,  151;    efficiency 

of,  23,  26;    single-stage,  152;    two-stage,  158,  159;    velocity  diagrams, 

155. 
Impulse-  and  reaction-turbine,  discussion  and  design,  195,  265. 
Isothermal  expansion,  30;  process,  41. 


Jet,  impulse  of,  5. 
"     reaction  of,  5,  74,  114. 


Kinetic  energy  of  jet,  4. 


K. 


Loss  of  velocity,  78. 

Losses,  frictional,  determination  of,  88. 

in  turbine,   182. 
Losses  in  Parsons  turbine,  distribution  of,  204. 
*'Lusitania."  Cunard  Steamer.  310-312. 


332  INDEX. 

M. 

Marine  steam-turbine,  295;   economy  of,  303,  304. 
Marine  steam  turbine,  application  of,  308. 
Marine  steam  turbines,  arrangements  of,  312. 
Mass,  3. 

"Mauretania,"  Cunard  Steamer,  310-312. 
Mollier,  heat  diagram,  53-60. 


N. 

Napier's  equation,  99. 

Nozzle,  calculations  of  dimensions,  85,  122;  "De  Laval,  114,  248;  divergent, 
69,  140;  experimental  work,  93,  123;  friction  in,  149;  ideal  expand- 
ing, 142;  vibrations  in,  146,  147. 

Nozzles,  design  of  Curtis  turbine,  171-175. 


O. 
Orifices,  experimental  work,  93,  102,  104. 

P. 

Parsons  turbine,  calculations  of  dimensions,  189. 

Parsons  turbine,  description,  252;  tests  of,  253,  254;  turbine-blades,  268. 

Parsons  turbine,  distribution  of  losses  in,  204. 

Peabody,  100. 

Peripheral  velocity,  21. 

Pressure,  curves  of  constant,  52;  dynamic,  6;  on  vanes,  11. 


R. 

Rankine,  99. 

Rateau,   100;    experiments,   106. 

Reaction,  26;  of  a  jet,  5,  74,  114;  nature  of,  67. 

Reaction-turbine,   general,   ix;    Hero's,   x;    discussion  and   design,   195; 

blades,  length  of,  214,  223;   velocity  diagrams,  221. 
Relative  velocity,  16. 
Resistance  to  flow  of  steam,  77. 
Revolution,  speed  of,  286. 
Rosenhain,  100,  107,  109. 
Rotor,  diameter  of,  217,  222. 


INDEX.  33a 

S. 

Sampling  tube  for  calorimeter,  242. 

Saturation  curve,  50. 

Sibley  College  experiments,  123;   apparatus,  141. 

Skin  friction,  139. 

Spacing  of  buckets,  126. 

Spindle,  diameter  of,  217,  222. 

Specific  heat,  44;    volume,  60. 

Speed  of  blade,  21. 

Steam,  flow  of,  27,  35,  62;  expansion  of,  30,  55;  superheated,  51,  57,  62; 

velocity  of,  curves,  160;   consumption,  181. 
Steam  turbines,  classification  of,  xiii. 
Steamship  propulsion,  308 


Temperature-entropy  diagram,  39. 

Tests  of  turbines,  Curtis,  ^282;  De  Laval,  250,  252;   Parsons,  253,  254. 

Thermodynamic  principles,  27. 

Torque  line  experimentally  determined,  178. 

Torsion  meters,  Denny-Johnson,  319. 

Torsion  meters,  Foettinger,  319. 

Turbine-buckets,  123;   Curtis,  163. 

Turbine  design,  general  remarks,  292. 

Turbine  testing,  water  brake  for,  319. 

Turbines,  types  of,  246. 


Vacuum,  gain  due  to  increase  of,  289. 

Vanes,  action  of  fluid  upon,  10;    change  of  direction  of  flow,  causing 

pressure  on,  11. 
Velocity,  calculation  of,  61,  64;    absolute,  21;    peripheral,  21;    relative, 

16,  21;   of  flow,  72,  114;   of  steam,  curves  of,  160;   loss  of,  78. 
Velocity,  ratios,  226. 
steam,  226. 
"Victorian"  and  "Virginian,"  steamers,  316-317. 
Volume,  specfic,  60. 


S34  INDEX. 

W. 

Water-brake  for  turbine  testing,  319. 
Wheels,  diameter  of,  170. 
Weight  of  flow,  64,  65,  71;  curve  of,  160. 
Wilson,  103,  107,  109;   apparatus,  140. 

Work,  done  on  vane  or  bucket  by  fluid,  20;  external,  28;  internal,  28; 
of  friction,  81. 

Z. 

Zeuner's  equation,  28,  35. 


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Los  Angeles 
This  book  is  DUE  on  the  last  date  stamped  below. 


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1953 


APR  8     1959 

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WAR  2  4  REC 
iV0V3  0  7953 

MAR  1  3 1961 


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